Physics

LIGHT  Optical Instruments

Key unit Competence

By the end of the unit, the learner should be able to analyse the functioning of simple and compound instruments and determine their magnifying power.

My goals

By the end of this unit, I will be able to:

* explain an optical instrument.

* explain the physical features of a human eye.

* describe the image formation by the eye.

* identify the physical features of a simple and compound microscope.

* explain the applications of simple and compound microscopes.

* differentiate between simple and compound microscopes.

* explain the operation of a lens camera and its application.

* explain the operation of a slide projector and its applications.

*describe the physical features of a telescope.

* list different types of telescopes.

* demonstrate the operation of telescopes.

* differentiate between telescopes and microscopes.

* identify the physical features of prism binoculars.

Introduction

Once the rules for predicting how rays travel through lenses have been discussed, guide your learners to discover that; a fantastic range of practical devices began to appear which aided the development of the modern world. The simple magnifying glass became the basis for telescopes, microscopes and spectacles. These devices were modified to improve the projection of images and with the discovery and development of light-sensitive chemicals, gave birth to modern photography and cinematography.

Definition of an optical instrument

Activity 1

(i) What objects (things) do you see in the classroom?

(ii) Move outside class and observe the kind of objects there, and write down atleast five of them.

(iii) Look at the distant objects.

Are you able to examine the objects in a more detailed manner?

Do you think you can be able to see these objects at night?

We use our eyes to see and view different objects. The eye cannot be used to view clearly these objects at night, and some distant objects or hidden objects. Objects which cannot be viewed by the eye can be focused using other instruments. All the instruments used to aid vision are called Optical instruments.

Man has always shown interest in observing things in a more detailed manner. In your early secondary, you looked at the uses of mirrors. We have also learnt in unit 1 of this book that lenses are used to focus objects. When the lenses or mirrors or both are arranged in a way, the arrangement can be used to observe objects in a more detailed manner. The arrangement makes what we call a compound optical instrument. The compound instruments include a compound microscope, telescopes, prism binoculars etc.

Angular magnification or magnifying power of an optical instrument

The human eye

The eye is a biological instrument used to see objects at different distances. It uses a convex lens system to form a small, inverted, real image of an object infront of it.

Structure of the eye

Activity 2

(i) In groups of two, look at one another’s eye.

(ii) Observe critically its external shape.

(iii) Observe it carefully and note its behaviour as one tries to see some objects in class.

Notice that the eye ball is round and fleshy.

Functions of the parts of the eye

The cornea: It is made out of a fairly dense, jelly like material which provides protection for the eye, and seals in the aqueous humour. It also provides most of the power of the eye (59 Dioptres), having about 46 Dioptres. So it provides most of the bending of light rays.

The aqueous humour: This is a waterly liquid that helps to keep the cornea in a rounded shape, similar to that of a lens.

The iris: This controls the amount of light entering the eye. The amount of light that enters the eye is one of the factors determining how focused an image is on the retina. The brighter the light the eye is exposed to, the smaller the iris’ opening will be. The brighter the light the eye is exposed to, the smaller the iris’ opening will be. The iris is the coloured part of the eye as seen from the outside. The iris opening or a gap through which light passes is called a pupil.

The lens: This is used to focus an image on the retina. It controls the bending of light rays by change of its shape, a process called accommodation, which is done by the ciliary muscles.

The ciliary muscles: These control the thickness of the lens during focusing. By contracting or squeezing the lens, they make it thicker and vice versa. Because the power of the lens is directly related to its thickness, the ciliary muscles change the power of the lens by their movement.

The retina: This is the light sensitive part of the eye and it is where images are formed. It contains millions of tiny cells which are sensitive to light. The cells send signals along the optic nerve to the brain. So the retina is the screen of the eye and the image is formed by successive refraction at the surfaces between air, the cornea, the aqueous humour, the lens and vitreous humour. The retina is black, which prevents any light rays that hit it from reflections and thereby changing the image.

The vitreous humour: This is a jerry like substance that helps the eye to keep its round shape. It is very close in optical density to the lens material.

The yellow spot: This is a small area on the retina where the sharpest image, that is, the finest detail can be seen.

The optic nerve: This is the nerve that transmits images received by the retina to the brain for interpretation. The part of the eye where the optic nerve joins the retina is called the blind spot because no images can be observed at at this point.

Visual Angle

Activity 3

(i) Go outside class and view the trees around.

(ii) Are the trees of the same height?

Notice that some trees at a distance, look shorter than the nearby trees when it is not the case? Why do you think it is so?Discuss and write down in your notebook about your observation.

The height of an object depends on the angle of elevation of its top from the eye. The larger the angle, the taller the objects. This angle is called the visual angle.

The visual angle is the angle subtended at the eye by an object.

Let us observe the flame of a candle: its two extremities A and B are seen by an eye at a certain angle. Expressed in radians, this angle has a measure:This angle decreases when the distance D increases and increases when the distance D decreases.It also increases when the length AB increases and decreases when AB decreases.

We call it visual angle of the object.Lead the learners to define the visual angle of an object as the angle between two rays of light from extremities of the object and penetrating into the eye of an observer.

Activity 4

(i) In groups of four, explain why trees in a forest appear to be of the same size.

Objects that subtend the same angle at the eye appear to be of the same size as viewed by the eye.

The apparent size of an object depends on the size of its image on the retina. For example, the two objects above; AB and CD appear to have same size because they subtend the same angle θ at the eye. This explains why trees in a forest appear to have the same height.

It is defined as the ratio of the apparent size of the final image i.e angle subtended by the image at the position of eye to the apparent size of the object i.e angle subtended by the object at the eye.

We have seen that we can use other instruments apart from the eye to aid vision. So, angular magnification or magnifying power of an optical instrument can also be defined as the ratio of the angle subtended at the eye by the image when the optical instrument is used to the angle subtended by the object at the unaided eye (when the instrument is not used).

If β is the angle subtended at the eye by the image and α is the angle subtended by the object at some distance by unaided eye, then the angular magnification

Accommodation of the eye

Accommodation of the eye is the ability of the eye to see near and distant objects. The eye is capable of focusing objects at different distances by automatic adjustment of the thickness of the eye lens which is done by the ciliary muscles. To focus a distant object, the eye lens is made thinner, so less powerful, and the rays from the object are brought to focus on the retina by the eye lens. In this case, the ciliary muscles are relaxed and pull the lens. For nearer objects, the eye lens must be made thicker and hence more powerful so that the rays from the near object can be brought to a focus on the retina. In this case, the ciliary muscles tighten and squeeze the lens.

Near point and far point of the eye

Activity 5

(i) Hold a book at an arm’s length and move it closer to find the nearest distance that you can focus the words clearly without straining your eyes.

(ii) Approximate the distance between your eyes and the book.

(iii) What does this distance represent?

The near point of the eye is the nearest point that can be focused by the un aided eye. It is a closest distance that the ‘normal’ human eye can observe clearly; without any strain to the eye. It is called the least distance of distinct vision. The near point of a normal eye is 25 cm.

Activity 6

(i) Look at the trees around your school.

(ii) Now, try to look at objects far from the school.

(iii) Are you able to focus the distant objects?

(iv) Measure this distance from the object to your eye.

(v) Write down your observation in the notebook.

Notice that you can not be able to measure this distance.

The distance from a distant object to the eye is the far point of the eye. The far point of the eye is infinity.

The far point is the farthest point that can be focused by the eye.

The distance of 25 cm from the eye is called distance of most distinct vision or least distance for distinct vision. The range of accommodation of the normal eye is thus from 25 cm to infinity. This range is based upon the average human eye which has an age of 40 years. Young persons have a much wider range but the average 70 year – old has a reduced range.

People with normal vision can focus both near and distant objects.

Defects of vision and their correction

Activity 7

(i) Have you seen before some people putting on eye glasses?

(ii) What do you think these glasses(spectacles) are used for.

People put on eye glasses for different reasons. Some people wear them in order to read a text, some put them on to see near objects if their eyes cannot be able to do so while others put them on so as to focus distant objects; others wear them for fan like sun goggles

Short-sightedness (myopia)

Activity 8

(i) Hold a book at an arm’s length and move the lens so that the prints are read without the eye getting strained.

(ii) Now, try to read the words on a chalkboard a distance from the book.

(iii) Are you able to focus both near and distant objects?

People with normal vision can focus clearly near and distant objects. Those who only focus near objects are said to be short-sighted, meaning that they see nearer.

Short-sightedness is the defect whereby a person can see near objects clearly but cannot focus distant objects. His far point is nearer than infinity. This is because the eyeball is too long or the lens is too strong so that rays of light from a distance object are focused in front of the retina.

The rays are focused in front of the retina because the focal length of the eye lens is too short for the length of the eye ball. This defect can be corrected by wearing a concave (diverging) spectacle lens. The rays of light from a distant object are diverged so that they appear to come from a point near, and so they are focused by the eye.

Rays from object at infinity appear to come from a near point F and converge to the retina.

Long-sightedness (hypermetropia)

This is where a person is able to see distant objects clearly but cannot focus near objects.

This is because either his eye ball is too short or the eye lens is too weak (thin) so that rays of light from a close object are focused behind the retina.

This eye’s near point is further than 25 cm.

The image of the near object is focused behind the retina because the focal length of the eye lens is too long for the length of the eye ball.

This defect can be corrected by wearing a convex lens spectacle. The rays of light from a near object are converged so that the rays appear to come from a point far, and so are focused by the eye.

Rays from a near object O appear to come from a distant object.

Presbyopia

Activity 9

(i) How many of you still have their grandparents?

(ii) Have you ever tried to observe how grand parents observe objects?

(iii) Discuss with your neighbour and write in your notebook results of your discussion.

When people grow older, their eye lens become stiff and it becomes hard for the ciliary muscles to adjust it. Such people have a defect called Presbyopia. Presbyopia is the stiffening of the eye lens such that it is less capable of being adjusted by the ciliary muscles. This means that the eye lens becomes less flexible and loses its power (ability) to accommodate for objects at different distances.

This defect is corrected by wearing bifocals spectacles whose lenses have a top part for looking at distant objects and a bottom part for close ones. These bifocal spectacles have a diverging top part to correct for distant vision and converging lower part for reading.

Astigmatism

This is the defect that occurs if the curvature of the cornea varies in different directions so that rays in different planes from an object are focused in different positions by the eye and the image is distorted. A person suffering from astigmatism sees one set of lines more sharply than others. This defect is corrected by wearing corrected lenses. These help to bend the incoming rays to correct for irregular refraction.

Example

The far point of the defective eye is 1m. What lens is needed to correct this lens. With this lens, at what distance from the eye is its near point, if the near point is 25cm without the lens?

Formation of an image by the eye

Light enters the eye through the transparent cornea, passes through the lens and is focused on the retina. The retina is sensitive to light and sends messages to the brain for interpretation. Although the image is inverted, the brain interpretes it correctly.

A lens camera

Activity 10

(i) Make a paper box and carefully use a pin to make a tiny hole in the centre of the bottom of the paper box.

(ii) Place a piece of wax paper on the open end of the box. Hold the paper in place with the rubber band.

(iii) Turn off the room lights. Point the end of the box with a hole in a bright window.

(iv) Look at the image formed on the wax paper.Which kind of image have you seen?

Is it upside down or right side up. Is it smaller or larger than the actual object? What type of image is it?

The image is upside down. The pin hole helps you to see the image of the object. This device is called a pin hole camera.

Activity 11

(i) When you were going to register for Rwanda National Examinations, you took some photographs.

(ii) What device did the person that took your photograph use?

In our daily lives, we take photographs. We use a lens camera to take these photographs.

Activity 12

(i) Enlarge the hole in the pinhole camera above at the front of the box and hold convex lens over the hole.

(ii) Adjust the position of the lens for either near or far objects to make a sharp image on the screen.

(iii) Is the image erect or inverted?

If the objects are coloured, is the image coloured?

Notice that the image formed is inverted and coloured if the object is coloured. By placing a lens above the hole, you are making a lens camera from a pin hole camera.

Formation of images by a lens camera

Activity 13

(i) Draw a ray diagram for the formation of an image of an object placed at a point beyond 2F of a thin converging lens.

(ii) State the nature and size of the image.

Is the image bigger or smaller?

We have already seen that when an object is beyond 2F of a thin converging lens, the image formed is smaller than the object.

A camera consists of a light- tight box with a convex (converging) lens at one end andthe film at the other end. It uses the convex lens to form a small, inverted, real image on the film at the back.

The lens focuses light from the object onto a light sensitive film. It is moved to and fro so that a sharp image is formed on the film. In many cameras, this happens automatically. In cheaper cameras, the lens is fixed and the photographer moves forwards and backwards to focus the object.

The diaphragm is a set of sliding plates between the lens and the film. It controls the aperture (diameter) of a hole through which light passes.In bright light, a small aperture is used to cut down the amount of light reaching the film and in dim light, a large hole is needed.Very large apertures give blurred images because of aberrations so the aperture has to be reduced to obtain clear images.In many cameras, the amount of light passing through the lens can be altered by an aperture control or stop of variable width. This size of the hole is marked in f – numbers i.e 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32. The smaller the f-number, the larger the aperture. An f-number of 4 means the diameter d of the aperture is ¼ the focal length, f of the lens. To widen the aperture, the f number should therefore be decreased.

The aperture also controls the depth of field of the lens camera. The depth of field is a range of distances in which the camera can focus objects simultaneously. This depth of field is increased by reducing the aperture.This large depth of field ensures a large depth of focus. The depth of focus is the tiny distance the film plane can be moved to or from the lens without defocusing the image. A large depth of focus means that both near and far objects appear to be in focus at the same time which is obtained by a small hole in the diaphragm.

The shutter controls the exposure time of the film. It opens and closes quickly to let a small amount of light into the camera.

The exposure time affects the sharpness of the image. When the exposure time is short, the image is clear (sharp) but when it is long the image becomes blurred.

The film. This is where the image is formed. It is kept in darkness until the shutter is opened. It is coated with light sensitive chemicals which are changed by the different shades and colours in the image. When the film is processed, these changes are fixed and the developed film is used to print the photograph.

Note that a diminished image is always formed on the film and that the image of distant object is formed on a film at distance f from the lens. For near objects, the lens is moved further away from the film (closer to the object) to obtain a clear image. In this case, the film is at a distance greater than f of the lens.

Activity 14

Discussion

In groups of four, discuss the differences and similarities between the lens camera and the human eye.How would you use a lens camera to make a million francs in one year?

The slide projector

Activity 15

(i) Have you ever seen an instrument called a slide projector?

(ii) What is that instrument used for?

A slide projector is an opto-mechanical device for showing photograhic slides

.Activity 16

(i) Have you ever watched a cinema where the pictures are seen on the white wall?

(ii) What device were they using to throw the pictures on the screen (wall or white cloth)?

(iii) Where do you think the pictures came from?

Are the images small or large?

The pictures are thrown on the screen using a slide projector.

A projector is a device used to throw on a screen a magnified image of a film or a transparent slide. It produces a magnified real image of an object.

It consists of an illumination system and a projection lens. The illumination system consists of a lamp, concave reflector and the condenser. The illuminant is either a carbon electric arc or a quartz lamp to give a small but very high intensity source of light in order to make the image brighter.

The lamp is situated at the centre of curvature of the mirror so that the rays are reflected back along their original path. The concave mirror reflects back light which would otherwise be wasted at the back of the projector housing. The condenser consisting of two Plano concave lenses collects light which would otherwise spread out and be wasted, and concentrates it on to the film (slide) so that it is very bright and evenly illuminated.

The light is then scattered by the film and focused by a convex projection lens on to the film. The projection lens is mounted in the sliding tube so that it is moved to and fro to focus a sharp image on the screen.

Example

1. A slide projector has a converging lens of focal length 20.0cm and is used to magnify the area of a slide, 5cm² to an area of 0.8m2 on a screen.

2. Calculate the distance of the slide from the projector lens.

Exercise

1. A colour slide has a picture area 2.4 cm x 3.6 cm. Find the focal length of the projection lens which will be needed to throw an image 1.2m x 1.8m on a screen 5m from the lens.

2. A projector projects an image of area 1 m² onto a screen placed 5m from the lens. If the area of the slide is 4 m², calculate;

(i) The focal length of the projection lens.

(ii) The distance of the slide from the lens

Activity 17

Make a projector on the bench using a ray box lamp, a single convex lens (focal length about 5 cm) for the condenser; a slide; a convex lens (focal length 5cm or 10cm) as the projection lens and a sheet of paper for the screen.Is the image inverted?By how much is it magnified?

Note that if the film is placed just after the lamp, the object would be poorly illuminated. So to give a bright picture, a condenser is included. The film O is placed between F and 2F of the projection lens so that the image I is real, inverted and magnified.

The film is put in the projector while it is upside down so that the picture on the screen is upright.

Microscope

Simple Microscope (Magnifying Glass)

Activity 18

(i) Hold a hand lens at above the word Rwanda at a distance of about 4cm from the word.

(ii) Move the lens farther away slowly from the word while observing the word through the lens

.(iii) What changes do you notice after observing?

(iv) Share ideas with your neighbour and write your observation in your notebook.

The word Rwanda becomes larger and larger and finally disappears. This word gets larger because of the lens. We say that it is being magnified by the lens.

Activity 19

(i) Place your hand on a table and hold a hand lens above it and do the same as in activity 18.

(ii) What do you notice?

Notice that the hair (fur) and other small holes on the skin are seen clearly. These parts of the skin are made bigger by the glass lens and this enables one to see them clearly. This lens which magnifies images is called a magnifying glass or a simple microscope.

A magnifying glass consists of a thin converging lens and It is used to view very small organisms or parts of organisms which cannot be easily seen by the naked eye.

Formation of images by a magnifying glass

Activity 20

Using the knowledge from thin lenses, draw a ray diagram to show the formation of an image by a magnifying glass.State the characteristics of the image formed.

We have already seen in unit 1 that when an object is between the lens and its principal focus, the image formed is magnified and upright. So, a magnifying glass forms a virtual, upright, magnified image of an object placed between the lens and its principal focus.

Activity 21

Making a simple microscope

(i) Use a pin or a nail to make a hole about 2 mm in diameter in a piece of a kitchen foil or glass.

(ii) Carefully let a drop of water fall on the hole so that it stays there and acts as a tiny lens with short focal length.

(iii) Use it to observe prints on a piece of paper.

Simple microscope (magnifying glass) in normal adjustment.

The magnification of a magnifying glass depends upon where it is placed between the user’s eye and the object being viewed and the total distance between them.

Activity 22

(i) Carefully place a magnifying glass above some prints on a piece of paper and adjust it until they are seen clearly.

(ii) Make sure that you don’t feel any strain in the eye while you are observing.

(iii) What do you think is the position of the image from the eye?

The image is at the least distance of vision since the eyes are not strained and the magnifying glass is said to be in normal adjustment.

A microscope is in normal adjustment if the final image is formed at the near point, and it is not in normal adjustment if the final image is at infinity.

Magnifying power of a simple microscope

We have already seen that the size of the image depends on the angle subtended by the object on the eye called the visual angle. Thus, the magnifying power depends on the visual angle

.It is defined as the ratio of the angle subtended by the image to the lens to the angle subtended by the object at the near point to the eye.

a) Magnifying power of a simple microscope in normal adjustment

Consider an object of height h placed at a given distance from the lens.Let β be the angle subtended by the image I to the lens.

This gives the maximum magnifying power of a simple microscope. Note that in calculations, the value of the magnifying power is negative. The negative sign can always be neglected since magnification cannot be negative.

The object distance can take any value in the range from the focal point to the point where it lies at the near point and if the object is at the focal point, then the object distance is equal to the focal length and the image is at infinity, and the microscope is not in normal adjustment.

b) Magnifying power of a simple microscope when it is not in normal adjustment

This is the minimum magnifying power of the simple microscope.

Note that, in this case, D is positive since it is of a real image from the eye, and from the formula, angular magnification is high for a lens of short local length.

Example

A magnifying glass has a focal length of 5cm. Find the angular magnification and the position of an object if the image is formed at the position of least distinct vision of 25cm.

Exercise:

1. Find the angular magnification produced by a simple microscope of focal length 5cm when used not in normal adjustment.

2. Explain why angular magnification of a simple microscope is high for a lens of short local length.

3. Why the image formed by magnifying glass is free from chromatic abberation.

Activity 23

In groups of five, discuss why the image formed in a magnifying glass is almost free of chromatic abbreviation.

When an object is viewed through the magnifying glass, various coloured images corresponding to IR, IV for red and violet rays are formed but each image subtends the same angle at the eye close to the lens and therefore these colours overlap. The overlap of these colours makes a virtual image seen in a magnifying glass free of a chromatic abberation.

Group Activity 24

In groups of five, go out side class and pick different kinds of leaves.Examine, with the use of a magnifying glass, the structures of the leaves.Discuss in detail the structural characteristics of each leaf.

Group Activity 25

You are provided with dirty water in a glass container.Use the magnifying glass provided and view some living organisms in it. Record what you see.

Activity 26

(i) Observe critically and describe the activity being done in the photograph.

(ii) State other uses of a magnifying glass.

Uses of magnifying glass: Magnifying glasses have many different uses. Some people use it for fun activities such as starting fires, or use the lens to help them read. You can start a fire with a magnifying glass when the sun rays are concentrated on the lens. Some retail stores sell reading glasses with the double convex lens. In everyday life, magnifying glasses can be used to do a variety of things. The most common use for magnifying glasses would be how scientists use them, they use magnifying glasses to study tiny germs

The compound microscope

Activity 27

Have you ever heard or seen an instrument called a compound microscope?What is it used for?

The compound microscope is used to detect small objects; is probably the most well-known and well-used research tool in biology.

Activity 28

Observe the above pictures carefully and in groups of three, discuss places where a compound microscope is used in daily life.

In daily life, microscopes are used in hospitals, in biology laboratories, etc.

Activity 29

(i) You are provided with two lenses of focal lengths 5cm and 10cm together with a half meter ruler and some plasticine.

(ii) Arrange the lenses as shown in the figure below.

(iii) Move the object to and fro until it appears in focus.

What do you notice about the image? Is it distorted? Is it coloured differently in any way?

By arranging the lenses as above, you have actually made a compound microscope.

We have already seen how a single lens (magnifying glass) can be used to magnify objects.However, to give a higher magnifying power, two lenses are needed.

This arrangement of lenses makes a compound microscope. It produces a magnified inverted image of an object

.A compound microscope is used to view very small organisms that cannot be seen using our naked eyes for example micro organisms.

A compound microscope consists of two convex lenses of short focal lengths referred to as the objective and the eye piece. The objective is nearest to the object and the eye piece is nearest to the eye of the observer.

The object to be viewed is placed just outside the focal point (at a distance just greater than the focal length) of the objective lens. This objective lens forms a real, magnified, inverted image at a point inside the principal focus of the eye piece. This image acts as an object for the eye piece and it produces a magnified virtual image. So the viewer, looking through the eye piece sees a magnified virtual image of a picture formed by the objective i.e of the real image.

Image formation in a compound microscope

An objective lens L₁ forms a real magnified image I, of an object O just placed outside its principal focus F0. I, is formed just inside the principal focus Fe of the eye piece L₂, which acts as a magnifying glass and produces a magnified, virtual image I₂ of I₁.

Compound microscope in normal adjustment (normal use)

Activity 30

You are provided with a bird's feather; observe it critically using a compound microscope and draw it in a fine detail.Make sure you observe the features when your eyes are relaxed.

When the eyes are relaxed, the image is at the near point and the compound microscope is said to be in normal adjustment.The compound microscope is in normal adjustment when the final image is formed at the near point (least distance of distinct vision), D of the eye.

Angular magnification (magnifying power) of a compound microscope

The magnifying power of a compound microscope is the ratio of the angle subtended by the final image to the eye when the microscope is used to the angle subtended by the object the unaided eye.

Angular magnification of a compound microscope in normal use

We have already seen that when a microscope is in normal use, the image I₂is formed at the least distance of distinct vision, D from the eye. Thus v = D.

From the above expression, it can therefore be seen that if f₀ and f_e are small, M becomes large. So the angular magnification M can be made high if the focal lengths of the objective and eye piece are both small.

Angular magnification of a compound microscope when not in normal use:

We have already seen that when a microscope is not in normal adjustment, the final image is formed at infinity i.e v = ∞.

Suppose that an object of height h is at a given position from the objective lens, forming an image of height h₁.

Example

A compound microscope has an eye piece of focal length 2.50cm and an objective of focal length 1.60cm. If the distance between the objective and eye piece is 22.1cm, calculate the magnifying power produced when the final image is at infinity.

Activity 31

Viewing specimens

The purpose of this exercise is to view micro organisms found in pond water while learning to operate a microscope.

Equipment

* Microscope

* Jar of pond water

* Slide

* Coverslip

* Dropper

Procedure

1. Collect a jar of pond water containing micro organisms. To ensure that you capture the largest number of micro organisms, do not simply scoop a jar of water from the centre of a pond. Instead, fill the jar partway with pond water and then squeeze water into the container from water plants or pond scum.

2. Prepare a specimen of pond water.

a) Using the dropper, place a few drops of pond water onto the centre of a clean, dry slide.

b) Hold the side edges of the coverslip and place the bottom edge on the slide near the drop of pond water.

c) Slowly lower the coverslip into place. The water should spread out beneath the coverslip without leaving any air bubbles. If air bubbles are present, you can press gently on the coverslip to move the air bubbles to the sides.

3. Set up the microscope.

a) Remove the dust cover from the microscope.

b) Plug in the microscope.

c) Turn on the microscope’s light source.

4. View the specimen with the low-power objective.

a) Move the slide around on the stage using your fingers or the control knobs until you find a micro organism.

5. View the micro organism with the high-power objective.

6. Sketch a picture of the micro organism.

7. Repeat steps 4, 5, and 6 until you have sketched atleast five different micro organisms.

8. Turn off the microscope.

a) Carefully, lower the objective to its lowest position by turning the coarse’ adjustment knob.

b) Turn off the light source.

c) Remove your slide. Clean the slide and cover slip with water.

d) Unplug the microscope and store it under a dust cloth.

Telescopes

Activity 32

You have heard in your early secondary that there are some heavenly and distant earthly bodies that cannot be seen by our naked eyes.

How did the people know that there exist such bodies?

Which instrument do you think is used to see these bodies and to observe what takes place on these bodies?

Why do you think it is difficult to see distant objects using our eyes?

Telescopes are instruments used to view distant objects such as stars and other heavenly bodies. Distant objects are difficult to see because light from them has spread out by the time it reaches the eyes, and since our eyes are too small to gather much light. There are two kinds of telescopes; refracting telescopes and reflecting telescopes.

Refracting telescopes

Activity 33

(i) Hold a convex lens of focal length 5cm close to your eye.

(ii) Hold another lens of focal length 20cm at an arm’s length.

(iii) Use the lens combination to view distant objects.

(iv) Adjust the distance of the farther lens until the image is clear (take care not to drop the lenses).

What type of image do you see?

The above lens combination is a refracting telescope. It is called a refracting telescope because it forms an image of the object by refracting light. Therefore, Refracting telescopes use lenses and they form images by refraction of light. Below are different kinds of refracting telescopes.

Astronomical telescope

The telescope made in the above activity is called an astronomical telescope. It consists of two convex lenses, the objective lens of long focal length and an eye piece lens of short focal length.

An astronomical telescope in normal adjustment

Activity 34

Using a telescope made in activity (30) above, view a distant object by moving the lenses so that the eyes are relaxed. What do you think is the position of the image?

When the eyes are relaxed, the image is at infinity and the telescope is in normal adjustment.

Therefore, an astronomical telescope is in normal adjustment when the final image is formed at infinity.

The rays of light coming from a distant object form a parallel beam of light. This parallel beam is focused by the objective lens and it forms a real, diminished image at its principal focus F_o. The eye piece is adjusted so that this image lies in its focal plane. This image acts as the object for the eye piece and the eye piece produces the image at infinity.

Note that in normal adjustment, the eye is relaxed or un accommodated when viewing the image. In this case, the eye has minimum strain.

Magnifying power or angular magnification of an astronomical telescope

The magnifying power of a telescope is the ratio of the angle subtended by the image to the eye when the telescope is used to the angle subtended at the unaided eye by the object.

Since the telescope length is very small compared with the distance of the object from either lens, the angle subtended at the unaided eye by the object is the same as that subtended at the objective by the object.

Angular magnification of an astronomical telescope in normal adjustment

In normal adjustment, the magnifying power (angular magnification) of an astronomical telescope is given by:

Note

(i) From the above expression, M is high when eye piece focal length f_e is short and the objective focal length f₀ is long. This explains the fact why the objective lens of long focal length and the eye piece lens of short focal length are used during the construction of the astronomical telescope.

(ii) For a telescope in normal adjustment, the separation of the objective and the eye piece is f₀ + f_e

Activity 35

In groups of four , discuss and give a summary of differences between a compound microscope and an astronomical telescope.

The table below shows the differences between a compound microscope and an astronomical telescope.

Example

An astronomical telescope has an objective lens of focal length 120 cm and an eye piece of focal length 5 cm. If the telescope is in normal adjustment, what is;

(i) The angular magnification (magnifying power)

(ii) The separation of the two lenses?

Exercise

An astronomical telescope is used to view a scale that is 300 cm from the objective lens. The objective lens has a focal length of 20cm and the eye piece has a focal length of 2 cm. Calculate the angular magnification when the telescope is adjusted for minimum eye strain.

An astronomical telecope with the final image at the near point

In this case, the image is seen in detail but the telecope is not in normal adjustment (use) because the eyes are strained.

The objective forms an image of a distant object at its focus F_o. The eye piece is moved so that this image is at a position inside its focus. This image acts as the object for the eye piece which acts as a magnifying glass and thus forms a magnified, virtual image.

Suppose that β is the angle subtended by the final image at the eye, and h1is the height of the image formed by the objective lens and that the angle subtended at the unaided eye is that subtended at the objective by the object, α For the eye close to the eye piece

The eye ring

The eye ring is the best position to place the eye in order to be able to view as much of the final image as possible.

The best position for an observer to place the eye when using a microscope is where it gathers most light from that passing through the objective.

In this case, the image is brightest and the field of view is greatest.In case of the telescope, all the light from a distant object must pass through the eye ring after leaving the telescope. So by placing the eye at the eye ring, the viewer is able to see the final image as much as possible.

Terrestrial telescope

Activity 36

(i) Did you notice that the final image in an astronomical telescope in activity (30) is inverted?

(ii) Place a convex lens in between the two lenses used to construct an astronomical telescope in activity (26) above.

(iii) Adjust the objective lens until the image is seen when the eyes are relaxed.What is the nature of the image? Is it upright or inverted?

An astronomical telescope produces an inverted image, so it is not suitable for viewing objects on the earth. It is suitable for viewing stars and other heavenly bodies. A terrestrial telescope provides an erect image and this makes it suitable to view objectives on the earth.

It consists of an erecting lens L of focal length f between the objective and the eye piece. The objective lens form an inverted image I₁. The lens L is placed at a distance of 2f from the image I₁. The image I₁ acts as the object and an erect image I₂ of the same size as I₁ is formed at 2 f beyond the erecting lens. This image I₂ acts as an object for the eye piece and in the usual way the eye piece forms the final image at infinity.

Note that the angular magnification of the terrestrial telescope is similar to that of the astronomical telescope because the erecting lens has no effect on the angular magnification produced but only inverts the image l₁so that the final image is upright.

Activity 37

In groups of four, discuss the advantages and disadvantages of a terrestrial telescope over an astronomical telescope.

The advantage a terrestrial telescope has over an astronomical telescope is that it produces an upright image.

However, the telescope is so long. It is much longer than other kinds of refracting telescopes. Its length is given by = f₀ + f_e+ 4_f.

The erecting lens also reduces the intensity of light emerging through the eye piece which makes the final image faint.

Galilean Telescope

Activity 38

Have you ever heard of a scientist called Galileo Galilee?What is he known for?

Galileo was a great scientist well known for his discoveries in astronomy.

Activity 39

(i) Hold a concave lens of focal length 5cm close to your eye.

(ii) Hold another convex lens of focal length 20cm at an arm’s length.

(iii) Use the lens combination to view distant objects.

(iv) What is the nature of the image?

The above lens combination is a Galilean telescope. A Galilean telescope consists of an objective lens which is a convex lens of long focal length and an eye piece which is a concave lens of short focal length. It forms erect images both in normal and not in normal adjustment.

Galilean telescope in normal adjustment

The objective lens would produce an image I₁ in the absence of the eye piece. With the eye piece in position at the distance f_e from I₁, I₁ acts as a virtual object to the eye piece and a virtual image of it is formed at infinity since 11 is at the focal point of the eye piece.

Angular magnification for a Galilean telescope in normal adjustment

Let h₁ be the height of image, l₁, β be angle subtended at the eye and α be the angle subtended at the unaided eye by the object which is very nearly equal to the angle subtended by the object at the objective lens.

Galilean telescope with final image at near point

The final image in a Galilean telescope can also be viewed at the near point of the eye when the telescope is not in normal adjustment.The final image in a Galilean telescope can also be viewed at the near point of the eye when the telescope is not in normal adjustment.

The objective lens forms the image l₁ at a distance greater than the focal length of the eye piece.

This image acts as a virtual object for the eye piece and an erect image of it is formed at a distance D.

Thus v = – D (since the image is virtual).

Activity 40

In groups of five, discuss the advantages and disadvantages of a Galilean telescope over an astronomical telescope and write them in your notebook.

Unlike in an astronomical telescope where the final image is inverted, the final image formed in a Galilean telescope is erect The telescope is also shorter than astronomical telescope and hence portable.

The distance between the lenses is given by f₀– f_e.On the other hand, a Galilean telescope has a small field of view and its eye ring is virtual (since the eye piece is concave) that is, it is between the lenses and so inaccessible to the eye.

Reflecting telescopes

Activity 41

In groups of four, go outside and observe a TV satelite dish in the neighbourhood.Discuss with your neighbour about the observation and present the report to the class.

Reflecting telescopes consist of a large concave mirror of long focal length as their objective. There are three kinds of reflector telescopes, all named after their inventors.

The Newtonian telescope is commonly used by amateur astronomers. A small plane mirror is used to direct the light from the concave mirror, which acts as an objective into an eye piece.

Rays from a distant object are reflected by the objective (concave mirror) to the plane mirror. This reflects the rays to form a real image I₁ which can be magnified by an eye piece or photographed by putting a film at I₁.

Note that the plane mirror deflects the rays of light side ways without changing the effective focal length f0of the objective.In normal adjustment, the angular magnification of the Newtonian reflection telescope is given by

Cassegrain reflecting telescope

This is the type used in most observatories It consists of a concave mirror which acts as an objective, a small convex mirror and the eye piece lens.Light from a distant object is reflected by the concave mirror to the convex mirror which reflects it back to the centre of the concave mirror where there is a small hole to allow the light through. So the convex mirror forms the final image (real) at the pole of the objective.

Coude Reflector Telescope

This is a combination of Newtonian and cassegrain reflector telescopes.

The plane and convex mirrors used in reflecting telescopes are used to bring the light to a more convenient focus where the image can be photographed and magnified several times by the eye piece for observation.

Activity 42

In groups of five, discuss the advantages of reflecting telescopes over refracting telescopes and write them in your notebook.

The reflecting telescopes are free from chromatic aberration since no refraction occurs.

The image formed is brighter than in refracting telescopes where there is some loss of light during refraction at the lens surfaces.

Spherical aberration can be eliminated by using a parabolic mirror instead of a spherical mirror as an objective.

They have a power because of higher ability to distinguish two closely related objects because of the large diameter of the parabolic mirror. We say that they have a high resolving power.They are easier to construct since only one surface requires to be grounded.

Critical Thinking Exercise

What is meant by the resolving power of an optical instrument?

Explain its usefulness

.Explain why astronomers use reflecting telescopes rather than refracting telescopes?

Prism binoculars

Activity 43

Have you ever asked yourself how tourists and scientists are able to see distant animals and birds in a forest or any hidden places?

Discuss with your neighbour and write in your notebook the observation.

Tourists and scientists use prism binoculars to view wild animals and birds in hidden places such as caves and forests.

These consist of a pair of refracting astronomical telescopes with two totally reflecting prisms between each objective and eyepiece. The prisms use total internal reflection to invert rays of light so that the final image is seen the correct way. These prisms reflect up and down the light and by doing so, they shorten the length of the instrument.

Prism A causes lateral inversion and prism B inverts vertically so that the final image is the same way round and same way up as the object. Each prism reflects light through 180o. This makes the effective length of each telescope three times shorter than the distance between the objective and the eye piece. So good magnifying power is obtained with compactness

Review Questions

1. (a) With the aid of a ray diagram, describe how a convex lens is used as a magnifying glass.

(b) Explain why an image formed in a magnifying glass is almost free from chromatic aberration.

2. (a) When is a compound microscope said to be in normal use?

(b) Derive an expression for the magnifying power of a compound microscope in normal use.

(c) Explain why the lenses that make up a compound microscope are of short focal lengths.

3. (a) When is a telescope said to be in normal adjustment.

(b) What is meant by the eye ring as applied to optical instruments.

(c) What are the differences between microscope and telescopes?.

4. (a) Explain why prisms are preferred to mirrors in prism binoculars.

(b) State the advantages of reflecting telescopes over refracting telescopes.

(c) The objective of an astronomical telescope in a normal adjustment has a diameter of 15cm and a focal length of 400cm. The eye piece has a focal length of 2.5cm. Find the magnifying power of the telescope.

5. (a) A distant objective subtending an angle of 3x 10-5 and in viewed with a reflecting telescope whose objective is a concave mirror of focal length 10m. The reflected light falls on a concave mirror placed 9.5cm from the pole of the objective which reflects the length back and a real image is formed a the pole of the objective where there is a hole. The image is viewed with a convex lens of focal length 5cm used as a magnifying glass which produces the final image at infinity.

6. How far must a 50mm focal-length camera lens be moved from its infinity setting to sharply focus an object 3m away?

7. Sue is far-sighted with a near point of 100cm. Reading glasses must have what lens power so that she can read a newspaper at a distance of 25cm? Assume the lens is very close to the eye.

8. A near-sighted eye has near and far point of 12cm and 17cm, respectively.

(a) What lens power is needed for this person to see distant objects clearly, and

(b) What then will be the near point? Assume that the lens is 2cm from the eye (typical for eye glasses).

9. What power contact lens is needed for an eye to see distant objects if its point is 25cm?

10. An 8cm focal-length converging lens is used as a “jeweler’s loupe”, which is a magnifying glass. Estimate (a) the magnification when the eye is relaxed, and (b) the magnification if the eye is focused at its near point N=25cm.

11. A compound microscope consists of a 10X eyepiece and 50X objective 17cm apart. Determine

(a) the overall magnification,

(b) the focal length of each lens, and

(c) the position of the object when the final image is in focus with eye relaxed. Assume a normal eye, so N = 25cm.

12. A near-sighted person cannot see objects clearly beyond 25.0cm (her far point). If she has no astigmatism and contact lenses are prescribed for her, what power and type of lens are required to correct her vision?

13. Microscope uses an eyepiece with a focal length of 1.4cm. Using a normal eye with a final image at infinity the tube length is 17.5cm and the focal length of the objective lens is 0.65cm. What is the magnification of the microscope?