◄Unit 1 :Thin lensesTopic 4►

Unit 2: Optical instruments

  • Unit 2: Optical instruments

    Key unit Competence 

    Describe and use optical instruments.

    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.

    INTRODUCTORY ACTIVITY

    When a patient goes to hospital having a headache and fever, a doctor may 
    require a blood test for malaria. When a sample of blood is taken, it is not 
    possible to check whether a patient has malaria or not. But a laboratory 
    technician may need to test the blood using some instrument and decide 

    whether the patient has malaria or not.

    Questions:

    (i) Which instrument do you think may be used to test malaria from 
    blood sample?
    (ii) In summary, discuss how that instrument function.

    (iii) What other instrument do you think can be used for such purpose?

    Introduction

    Once the rules for predicting how rays travel through lenses have been 
    discussed; 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 2.1 

    In our daily activities and development, we observe different things in 
    environment or in universe. Sometimes, some objects cannot be easily 
    observed using our naked eyes. We need to see these very small things at 
    big distance.
    (i) What do you think we use to observe those distant or very small 
    bodies?
    (ii) Discuss the properties used by those instruments?
    (iii) Name at least four instruments that people use to observe distant or 

    very small objects.

    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.

    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.

    C

    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.

    Angular magnification or magnifying power of an optical 

    instrument

    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.

    c

    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.

    C

    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.

    C

    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.

    C

    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.

    C

    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?

    C

    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.

    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.

    C

    C

    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

    C

    Objects that subtend the same angle at the eye appear 

    to be of the same size as viewed by the eye.

    C

    Application activity 2.1

    1. Name the part of the eye 
    a) which controls how much light enters it, 
    b) on which the image is formed, 
    c) which changes the focal length of the crystalline lens. 
    2. A farsighted person has a near point of 100 cm. Reading glasses 
    must have what lens power so that this person can read a 
    newspaper at distance of 25 cm? Assume the lens is very 
    close to the eye.
    3. A nearsighted eye has a near and far point of 12 cm and 17 cm, 
    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 2.0 cm from the eye (typical for eyeglasses).

    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?

    C

    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 and the film at the other end. It uses the convex lens to form a small, 

    inverted, real image on the film at the back.

    c

    C

    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. Digital cameras are similar to film cameras except that the light does not 
    form an image on photographic film. The image in a digital camera is formed 

    on a charge-coupled device (CCD).

    C

    The CCD is the light-sensitive component of the camera. In a nondigital

    C

    C

    C

    Application activity 2.2

    1. A camera gives a clear image of a distant landscape when the lens 
    is 8 cm from the film. What adjustment is required to get a 
    good photograph of a map placed 72 cm from the lens?

    2. The lens of a certain 35 mm camera (where 35 mm is the width of 
    the film strip) has a focal length of 55 mm and a speed (an 
    f-number) of f/1.8. The correct exposure time for this speed 
    under certain conditions is known to be (1/500) s.

    a) Determine the diameter of the lens.
    b) Calculate the correct exposure time if the f-number is 

    changed to f/4 under the same lighting conditions.

    The slide projector

    Activity 14

    (i) Have you ever seen an instrument called a slide projector?
    (ii) What is that instrument used for?
    (iii) Have you ever watched a cinema where the pictures are seen on the 
    white wall?
    (iv) What device were they using to throw the pictures on the screen 
    (wall or white cloth)?
    (v) Where do you think the pictures came from?

    (vi) Are the images small or large?

    C

    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.

    C

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

    C

    C

    Application activity 2.3

    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 cm2
    , calculate;
    (i) The focal length of the projection lens.

    (ii) The distance of the slide from the lens

    Activity 15

    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 16

    (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.

    C

    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 17

    (i) Place your hand on a table and hold a hand lens above it and do the 
    same as in activity 16.

    (ii) What do you notice?

    C

    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 18

    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 19

    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 20

    (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

    C

    V

    C

    C

    C

    C

    Application activity 2.4

    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 21

    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 22

    Provided a magnifying glass, go outside and pick different kinds of leaves. 
    Examine, with the use of a magnifying glass, the structures of the leaves. 

    Discuss in details the structural characteristics of each leaf

    Group Activity 23

    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 24

    C

    (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 25

    Have you ever heard or seen an instrument called a compound 
    microscope?

    What is it used for?

    C

    The compound microscope is used to detect small objects; is probably the 

    most well-known and well-used research tool in biology. 

    Activity 26

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

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

    Activity 27

    (i) You are provided with two lenses of focal lengths 5cm and 10cm 

    together with a half meter ruler and some plasticine. 

    C

    (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.

    C

    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

    V

    C

    Compound microscope in normal adjustment (normal use)

    Activity 28

    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 I2

    is formed at the least distance of distinct vision, D from the eye. Thus v = D.

    C

    Consider an object of height h at a given distance slightly greater than the 

    focal length of the objective lens. 

    C

    C

    C

    V

    C

    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.

    C

    Activity 29 
    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.

    C

    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. 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.

    Application activity 2.5

    A compound microscope consists of a 10× eyepiece and 50× objective 
    17.0 cm apart. Determine (a) the overall magnification, (b) the focal length 
    of each lens, (c) the position of the object when the final image is in focus 

    with the eye relaxed. Assume a normal eye, so N = 25 cm.

    Telescopes

    Activity 30

    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 31

    (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 32

    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.

    C

    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 Fo
    . 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.

    C

    C

     Activity 33

    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.

    C

    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?

    C

    Application activity 2.6

    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.

    C

    C

    C

    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 

    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.

    C

    Activity 34

    Discuss the advantages and disadvantages of a terrestrial telescope over 

    an astronomical telescope.

    C

    Galilean Telescope 

     Activity 35

    (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.

    C

    C

    C

    C

    Activity 36

    Discuss the advantages and disadvantages of a Galilean telescope over an 

    astronomical telescope and write them in your notebook.

    C

    Reflecting telescopes

    Activity 37

    Take the case of a TV satellite dish in the neighborhood. Discuss and 

    explain the functioning and principle of a satellite dish

    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.

    C

    C

    Cassegrain reflecting telescope

    C

    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.

    C

    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 38

    Discuss and explain the advantages of reflecting telescopes over refracting 

    telescopes.

    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 39

    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.

    C

    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.

    END UNIT ASSESSMENT

    1. A certain nearsighted person cannot see distinctly objects beyond 80 
    cm from the eye. What is the power in diopters of the spectacle lenses 

    that that will enable him to see distant objects clearly?

    2. Explain the difference between the terms magnifying power and 
    magnification, as used about optical systems. Illustrate this, by 
    calculating both, in the case of an object placed 5.0 cm from a simple 
    magnifying glass of focal length 6.0 cm, assuming that the minimum 

    distance of distinct vision for the observer is 25 cm.

    3. An eyepiece is made of two positive thin lenses, each of focal length f 
    = 20 mm, separated by a distance of 16 mm. 
    (a) Where must a small object viewed by the eyepiece be placed so 
    that the eye receives parallel light from the eyepiece? 
    (b)Does the eye see an erect image relative to the object? Is it 
    magnified? 

    (c) Use a ray-trace diagram to answer these questions by inspection.

    4. A common telephoto lens for a 35 mm camera has a focal length of 
    200 mm; its range from to (a)What is the corresponding range of 
    aperture diameters? (b)What is the corresponding range of image 

    intensities on the film?

    5. What is the maximum stop rating of a camera lens having a focal 
    length of and a diameter of ? If the correct exposure at , what 

    exposure is needed when the diaphragm setting is changed to ? 

    ◄Unit 1 :Thin lensesTopic 4►