THIN LENSES
 The figure below shows how a distant object is focused in a defective eye.
 i) State the nature of the defect.
 ii) Suggest suitable lens to correct the defect.
 a) You are provided with a rectangular glass block, two pins and a piece of white paper. Describe how you would use them to determine the refractive index of the glass using real and apparent image method.
 b) An object O is placed 15cm from a converging lens of focal length 10cm.
 i) At what distance should a screen be placed so that a focused image is formed on it?
 ii) A diverging lens of focal length 37.5 cm is placed half way between the converging lens and the screen. How far should the screen be from the diverging leans in order to receive a focused image?
 c) Two lenses L_{1} and L_{2} placed 12cm from each other. The focal length of L_{2} is 4cm. An object 5mm high is placed 4cm from L_{1}.
 i) Construct a scaled ray diagram on a graph paper to obtain the position of the final image as would be observed by a person on the right hand side of L_{2}
 ii) Determine the magnification obtained by the arrangement.
 The figure below represents and object O placed 10cm in front of a diverging lens. F is the focal point of the lens.
Draw rays to locate the position of the image. Determine the image distance.
 A vertical object is placed at the focal point F of a diverging lens as shown in figure 16.
Sketch a ray diagram to show the image of the object.
 a) Describe with the aid of labeled diagram an experiment to determine the focal length of the lens when provided with the following; an illuminated object, a convex lens, a lens holder, a plane mirror and a metre rule.
 b) A small vertical object is placed 28cm in front of a convex lens of focal length 12cm. On the grid provided, draw a ray diagram to locate the image. The lens position is shown. (Use a scale: 1 cm represents 4 cm).
 c) Fig. 1 shows a human eye with a certain defect.
 i) Name the defect.
 ii) On the same diagram, sketch the appropriate lens to correct the defect and sketch rays to show the effect of the lens.
 a) Figures 11 (a) and (b) show diagrams of the human eye.
 i) Sketch in figure 11(a) a ray diagram to show short sightedness.
 ii) Sketch in figure 11(b) a ray diagram to show how a lens can be used to correct the shortsightedness. (2mks)
 b) Figure 12 shows the features of a simple camera.
 i) Name the parts labelled A and B.
 ii) A still object is placed at a certain distance from the camera. Explain the adjustments necessary for a clear image of the object to be formed.
iii) State the functions of the shutter and the parts labelled A and B
 c) A lens forms clear image on a screen when the distance between the screen and the object is 80cm. If the image is 3 times the height of the object, determine
 i) The distance of the image from the lens.
 ii) The focal length of the lens.
 An image formed on a screen is three times the size of the object. The object and the screen are 80cm apart when the image is sharply focused. Determine the focal length of the lens.
 A luminous object and a screen are placed on an optical bench a converging lens is placed between them to throw a sharp image of the object on the screen, the magnification is found to be 2.5. The lens is now moved 30cm nearer to the screen and a sharp image is again formed. Calculate the focal length of the lens.
 An object is placed 16cm from a converging lens of focal length 12cm. Find.
(i) Position of image.
(ii) Nature and
(iii) Magnification of the image.
 An object is placed 15cm from a diverging lens and the image is formed 6cm from the lens. What is the focal length of the lens?
 Calculate the power of a lens whose focal length is given as 10cm.
 Explain differences between the eye and the camera. State also the similarities.
 (a) A lens forms an image four times the size of the object on the screen. The distance between the object and the screen is 60cm when the image is sharply focused.
(i) State with a reason what type of lens was used.
Determine:
(i) The object distance.
(ii) The image distance.
 The figure below shows the basic parts of a simple lens camera.
(i) Name the parts labeled A and B.
(ii) State the function of each of the parts A and B.
 (a) A defective eye focuses a near object as shown in the figure below.
(i) State the defect.
(ii) Suggest a suitable lens that can be used to correct the defect.
(iii) Draw a diagram to illustrate the correction of the defect.
(b) (i) A real image, half the size of the object is formed by a lens. If the distance between the object and the image is 450mm, determine the focal length of the lens.
 The figure below shows a virtual image formed by a convex lens. Complete the ray diagram to show the position of the object.
 The figure below shows an object placed in front of a concave mirror of focal length 10cm. C is the centre of curvature.
 (i) On the same figure draw a ray diagram showing the position of the image.
Use the ray diagram (i) above to determine:
(ii) The images distance:
(iii) Magnification:
 A vertical object is placed 20cm in front of a convex lens of focal length 5cm.
Determine:
 The image distance:
 The Magnification
 State two characteristics of the image.
 Joan performed an experiment to measure the focal length of a convex lens. A series of object distances (u) and image distance (v) were recorded and then a graph of uv against u+v was drawn; as shown.
(i) Show that the slope of the graph is equal to the focal length.
(ii) Determine the focal length of the lens from the graph.
 a) An object 5 cm high is placed at the principal focus of a concave lens of focal length 20 cm. By construction, locate the image and describe it fully.
 How far should the object be placed from the lens in order to obtain an image that is two times the object size?
 b) Figure 5 below shows one of the common eye defects.
 i) State the type of defect and the possible cause.
 ii) On the same diagram, show how the defect can be corrected.
 c) Draw a ray diagram to show how a convex lens works as a magnifying glass.
 Figure 7 below shows a human eye with a certain defect.
 i) Name the defect.
 ii) On the same diagram, sketch the appropriate lens to correct the defect.
iii) Sketch rays to show the effect of the lens (ii) above.
 iv) State two causes of the defect above.
 a) The figure below shows one of the common eye defects.
 State the type of defect and its possible cause.
 Show on the diagram how the defect can be corrected.
 An object of 5cm stands before a diverging lens of focal length 15 cm and at a distance of 10 cm from the lens. Determine
 The image distance.
 The magnification due to the lens.
(c) The diagram below shows a curved mirror.
 What type of mirror is it?
 By use of rays, locate the image of the object shown on the diagram
 A vertical object is placed at the focal point F of a diverging lens as shown in figure 3.
Fig. 3
Sketch a ray diagram to show the image of the object.
 The figure below shows the relationship between the reciprocal of the object distanceand the reciprocal of the image distance () for an object placed in front of a concave lens.
From the graph, determine the focal length of the lens.
 a) The figure below shows an object placed in front of a thin lens. The focal length of the lens is 10cm.The screen is adjusted until an image which is magnified 5 times is obtained.
From the information
(i) Which type of lens was in the experiment?
(ii) State any other characteristic of the image formed.
(iii) Find the value of u
 b) The figure below shows an object and an image formed by a certain lens.
By drawing suitable rays
(i) Locate the position of the focal point F of the lens.
(ii) Find the value of focal length f.
 c) The figure below shows a defective eye
object Image
(i) State the cause of the defect.
(ii) What type of lens is used to correct the defect?
 d) State any two similarities between an eye and a camera.
(c) The figure below shows two converging lenses L1 and L2 placed 8cm from each other. The focal length of the lens L1 is 2cm and that of L2 is 2.8cm. An object 1.0cm high is placed 3cm from the lens L1.
 On the graph paper provided construct a ray diagram to show the position of the final image as seen by the eye of a person.
 Determine the magnification obtained by this arrangement.
(d) State two applications of a fibre optic cable.
 The figure below shows a human eye with a certain eye defect:
(i) Name the defect………
(ii) On the same diagram, sketch the appropriate lens to correct the defect and sketch rays to show the effect of the lens.
 (a) Sketch a diagram to illustrate how a convex lens is used as a magnifying glass.
 The table below shows values of image distance, V and magnification (m) for a convex lens.
Magnification, M  0.09  0.4  0.78  1.49  1.74 
Image distance Vcm  4.41  5.62  7.10  10.05  11.10 
(i) In the grid provided, plot a graph of magnification M (yaxis) against image distance V.
(ii) Given the equation M = ^{V}/_{f } 1, determine the total length f, from the graph.
 (a) With the aid of a labelled diagram, explain how the focal length of a convex lens may be estimated by focusing a distant object.
(b) The graph below shows values obtained in an experiment to determine the focal length of a convex lens. Use the graph to determine the focallength of the lens.
GRAPH OF AGAINST
(c) An object is placed 30cm infront of a converging lens of focal length 20cm.
(i) By calculation determine the position of the image.
(ii) State the nature of the image
 (a) The figure below shows how an image is formed by a converging lens.
 State the value of the focal length of the lens.
 Calculate the magnification of the image produced.
(b) The figure shows a glass lens in air and its two focal points F_{1} and F_{2}.
Three rays of light pass through F_{1} to the lens.
 On the figure continue the three rays through the lens and into the air.
 State what happens to the speed of light on entering the glass lens from air.
(c) A ray of light passes through one surface of a glass prism at right angles to the surface, given that the critical angle of the glass material is 42^{0}, complete the ray to show how it travels until it leaves the prism. (
 An object is placed 30cm infront of a convex mirror of focal length 20cm. Determine the image distance.
 (i) State two possible causes of long sightedness.
(ii) What type of lens is used to correct long sightedness?
 In an experiment with a convex lens, image distances were measured when an object was placed at various distances away from the lens. The figure below shows a graph of 1/v against 1/u for the experiment where u is the object and v is the image distance.
Use the graph to find the focal length f of the lens
 Figure 14 shows a human eye with a defect
Figure 14
 (i) Name the defect of the eye
(ii) Describe how the defect in i) above can be corrected
 In an experiment to determine the focal length of converging lens a student plotted a graph shown.
Use the graph to determine the focal length of the lens used by the student
 The graph below shows the variation of magnification M with image distance v for a concave mirror.
Determine:
(i) The object distance when the image is 45 mm
(ii) The focal length of the mirror
 a) Some students wish to determine the focal length of a convex lens of thickness 0.6cm using an optical pin and a plane mirror. Figure 6 shows the experimental set up when there is no parallax between the pin and the image.
(i) Determine the focal length of the lens.
(ii) Explain how you arrive at your answer.
 b) An optician in Eldoret Hospital examined an eye of a patient and made the following observations:
Eye ball too short and the focal length of the eye lens too short
(i) State the eye defect the patient could be having.
(ii) Use a diagram to describe how the defect could be corrected.
 c) The graph below shows the variation of 1/v and 1/u in an experiment to determine
the focal length of a lens.
(i) Use the graph to determine the focal length.
(ii) What is the power of the lens used?
 b) A form four student resists sitting far away from the chalkboard and scrumbles for the front seat all the times. What eye defect could this student be suffering from. Draw a sketch diagram to show how this defect can be corrected
 (a) The diagram below shows an experimental set up consisting of a mounted lens, L, a screen, S, a metre rule and a candle.
Fig 6
(i) Describe how the setup may be used to determine the focal length, f of the lens.
(ii) State the reason why the setup would not work if the lens were replaced with a diverging lens
(b) The graph below shows the relationship between and for converging lens where u and v are the object and image distances respectively.
From the graph, determine the focal length, f, of the lens.
(c) An object placed 15cm from a convex lens is magnified two times. Determine the focal length of the lens. (3mks)
 a) Sketch on a diagram to illustrate how a convex lens is used as a magnifying glass.
 b) The table below shows values of image distance (v) and magnification (m) for a convex lens.
Magnification (m)  0.09  0.4  0.78  1.49  1.74 
Image distance (v) (cm)  4.41  5.62  7.10  10.05  11.10 
(i) On the grid provided below, plot a graph of magnification m (y – axis) against image distance ( v).
(ii) Given the equation , determine the focal length f from the graph.
 c) Draw a diagram to illustrate the defect corrected by a concave lens. Explain using a diagram how the defect is corrected.
 A vertical object O is placed at the principal focus F of a diverging lens as shown in Fig. I
Complete the diagram by drawing appropriate rays to show the image formed.
 (i) The sketch below shows an object placed some distance from a biconcave lens.
Draw rays to locate the image on the diagram
(ii) A biconcave lens forms an erect image twice the size of the object. If the focal length of the lens is 20cm, determine the object distance.
 The graph below is a plot of image distance against the object for a concave lens
Fig 4

From the graph determine the focal length of the concave lens.
(b) A biconvex lens forms an erect image twice the size of the object if the focal length of the
lens is 20cm. Determine the object distance
(c) (i) State one application of a convex lens where the object is positioned between
principal focus and the centre of curvature
(ii) In a compound microscope the objective lens has a focal length of 8mm and the
eyepiece lens has a focal length of 25mm. An object is placed at a distance of
12mm in front of the objective lens. If the system forms a final image that is
100cm from the eyepiece, determine the distance of separation of the two lenses
 Figure 10 below shows an object in front of a lens.
 Using rays locate the image of the object as seen by observer E.
 Give one application of such a lens as used above.
 Write three similarities between an eye and a camera
 b) Figure 11 (a) and (b) show diagram the human eye
 In figure 11 (a) sketch array diagram showing long sightedness
 In figure 11 (b) sketch array diagram showing how a lens is used to correct the long sightedness.
 c) A object of height 10.5cm stands before a diverging lens of focal length 20cm and a distance of 10cm from the lens. Determine.
 i) Image distance
 ii) Height of the image
iii) Magnification
 a) The figure below shows rays of light entering a human eye which has a defect.
eye
 name the defect
 State 2 possible causes of the defect.
 In the space below, draw a ray diagram to show how the defect can be corrected.
 b) A small bright object O lies at the bottom of a beaker containing water of depth h. A convex lens of focal length 15cm is held at the surface of the water. With this arrangement the image of O is formed at a point 45cm from the water surface as shown in the figure below.
image
45cm
lens
h
object
Taking the refractive index of water to be 4/3. Determine
 the apparent depth of the object
 the real depth h, of the object
 A ray light is incident at right angles at the face AB, of a right angled isosceles prism of
refractive index 1.6 as shown in the figure below.
Liquid
A C
Liquid Liquid
B
If the prism is surrounded by a liquid of refractive index 1.40; determine:
 The angle of incidence ion the face BC.
 The angle of refraction on the face BC.
 (a) An object 2cm tall is placed 22.5cm from a convex lens of focal length 15cm. on the other side of the converging lens, a diverging lens of focal length 30cm is placed such that the distance between the lenses is 35cm.
Determine by scale drawing on the grid provided.
(i) The position of the final image.
(ii) The total magnification.
(b) The diagram below represents a human eye receiving light from (a) a distant source (b) a point 45cm from the eye (c) a point 25cm from the eye.
(i) Name the eye defect.
(ii) What type of spectacles would be required for correction?
Determine its focal length.
 (a) When does a convex lens form a virtual image
(b) Figure 8 shows an object ‘O’ in front of a lens.
(i) By drawing appropriate rays on the same figure state the position of the image
formed
(ii) Explain the adjustments you would make on the position of the object above in order to obtain a real magnified image
 An object 1cm tall standing 10cm from a converging lens produces a magnified image 2.5cm tall on the same side as the object. Determine the focal length of this lens
 The figure below shows how a near object O is focused in a defective eye,

 a) What problem does the observer face when viewing an object at the near point?
 b) (i) Sketch on the same figure how a distant object is focused by the eye.
(ii) State the nature of the defect.
 c) (i) A pastor is known to have the defect stated in (b) (ii) above how will the pastor handle a bible as he read
(ii) How would you advise the pastor as he goes about correcting the defect?
 The graph in figure 7below shows the relationship between magnifications of the image against image distance of a convex lens. Use the formation on the graph to answer questions that follow
Fig 7
 Given that the lens formula is, write down the equation of the graph.
 Determine the object distance when m =1.0
 Determine the focal length of the lens
 The distance between an object and its magnified real image produced by a concave mirror is 20cm. When the object is placed 10cm from the pole of the mirror.
Determine
 i) Linear magnification of the image
 ii) The focal length of the mirror