1. Define the following terms as used in curved lens.

i) Principal focus (F). (1mk)

ii) Focal length (f) (1mk)

2. Distinguish between a real and a virtual image.

3. A boy scout wanted to light up his match stick using a lens. State the type of
lens he should use and explain how? ( 3mk)

4. State one similarity and one difference between a concave lens and a convex
mirror (2mks)

5. State one similarity and one difference between a diverging lens and convex
mirror (2mk)

6. Under what conditions does a converging lens form

(i) Real images (1 mk)
(ii) Virtual images (1 mk)

7. State one application of a convex lens where the object is positioned between
principal focus and the centre of curvature (1mk)

8. Sketch on a diagram to illustrate how a convex lens is used as a magnifying

glass. (3mks)

9. An object is placed at 2F in front of a converging lens and its image is observed.

State how the image changes as the object is moved from 2F towards F.

10. Show that the linear magnification M of a convex lens is given by

V
M= −1
f (2mks)

11. 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.

12. You are provided with a metre rule, distant object, concave mirror and a white
screen. Briefly describe how you can estimate the focal length of the focal
length of the concave mirror. (3mks)

13. An object is placed 20cm in front of a concave lens of focal length 15cm. State
two characteristics of the image formed.

FORM4 THIN LENSES Pg1

 14. The diagram below shows an experiment set up to determine the focal length of
a converging lens.

Describe how the set up may be used to to determine the focal length, f, of the
lens. (5 mks)

15. The diagram below shows an experimental set up consisting of a mounted lens,
L, a screen, S, a metre rule and a candle.

S
Candle L

Ruler

(i) Describe how the set-up may be used to determine the focal length, f of
the
lens. (5mk)
(ii) State the reason why the set-up would not work if the lens were replaced with a
diverging lens (1mk)

16. Figure below shows an object in front of a lens.

O
2F F F 2F

(i) Using rays locate the image of the object.

(ii)Give one application of such a lens as used above.
17. Figure shows a convex lens. An object is placed infront of the lens such that a
real magnified image is formed by the lens. Sketch on the same diagram a ray
diagram to represent this

FORM4 THIN LENSES Pg2

 C

18. Figure shows an object ‘O’ in front of a lens.

2F F F 2F

(i) By drawing appropriate rays on the same figure state the position of
the image formed (3mk)
(ii) Explain the adjustments you would make on the position of the object
above in order to obtain a real magnified image (2mk)
19. The sketch below shows an image formed some distance from a biconvex lens.
Complete the ray diagram to locate the object.

Image

20. The diagram in figure shows an object O placed in front of a converging lens. F
and Fare theprincipal foci for the lens.

FORM4 THIN LENSES Pg3

 The object is now moved along the principal axis until a virtual image is produced.
(i) Draw the object O in the new position along the principal axis. (1mk)
(ii) Sketch rays to show formation of the virtual image. (2mks)

21. Fig shows an image I formed by a concave lens. F and F1 are the principal foci.

I
F F1

Complete the diagram to locate the position of the object. (2mk)

22. The figure below represents and object O placed 10cm in front of a diverging
lens. F is the focal point of the lens.

O F

Draw rays to locate the position of the image. Determine the image distance.
23. The figure below shows two converging lenses L 1 and L2 placed 8cm from each
other. The focal length of lens L1 is 2cm and that L2 is 2.8cm. An object 1.0cm
high is placed 3cm from lens L1 L2
L1

O Eye
FORM4 THIN
3cm LENSES Pg4
 (i) On the grid below, construct a ray diagram to scale to show the position
of the final image as seen by the eye of the person (4mk)
(ii) Determine the position of the final image formed from lens L2and state
its nature
(iii) Determine the magnification obtained by this arrangement (4mk)
24. The diagram shows an arrangement of lenses; L o and Le used in a compound
microscope F0 and Fe are principal foci of L0 and Le respectively. Draw the rays
to show how the final image is formed in the microscope. (3mk)
L0

L0

Fo Fe Fe
O
Fo

25. 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. (4mk)
(ii) The total magnification. (2mk)
26. Two lenses L1 and L2 placed 12cm from each other. The focal length of L 2 is 4cm.
An object 5mm high is placed 4cm from L1.
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 L2
ii) Determine the magnification obtained by the arrangement

27. The sketch below shows an object placed some distance from a biconcave lens.

FORM4 THIN LENSES Pg5

 Draw rays to locate the image on the diagram (2mk)
28. A vertical object O is placed at the principal focus F of a diverging lens as
shown.

F F

Complete the diagram by drawing appropriate rays to show the image formed.
(3mks)
29. Figure below shows a real image formed by a convex lens.

I
F F

On the same grid, construct a ray diagram to locate the position of the object
(3mks)
THEEYE
1. Define the term “accommodation” as applied to human eye.

2. State ONE similarity and ONE difference between a camera and a human eye.

3. State two possible causes of long sightedness. (2 mks)

4. An optician in Eldoret Hospital examined an eye of a patient and made the

following observations: Eye too short and the focal length of the eye lens too
short.
(i) State the eye defect the patient could be having. (1mk)

FORM4 THIN LENSES Pg6

 (ii) Use a diagram to describe how the defect could be corrected. (2mk)

5. A form four student resists sitting far away from the chalkboard and scrambles
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 (5mk)

6. A man needs to hold a newspaper at arm’s length in order to read it.

a) State a likely defect of vision which would cause this. (1 mk)
b) State the type of spectacle lens that is required to correct this. (1 mk)

7. The figure below shows how a distant object is focused in a defective eye.

i) State the nature of the defect. (1mk)

ii) On the same diagram, sketch the appropriate lens to correct the defect and
sketch rays to show the effect of the lens. (2mk)
(iii) State 2 possible causes of the defect. (1mk)
8. Figures (a) and (b) show diagrams of the human eye.

(a) (c)

(d)
(b)

i) Sketch in figure (a) a ray diagram to show short sightedness and in (b)
sketch array diagram showing long sightedness (2mk)
ii) Sketch in figure (c) a ray diagram to show how a lens can be used to
correct the shortsightedness and in (d)sketch array diagram showing
how a lens is used to correct the long sightedness.. (2mks)
9. Figure shows the features of a simple camera.

A
Lens
B

Shutter

FORM4 THIN LENSES Pg7

 i) Name the parts labelled A and B. (2mks)
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.
(2mks)
iii) State the functions of the shutter and the parts labelled A and B (3mk)

10. Write three similarities between an eye and a camera

11. Explain differences between the eye and the camera. State also the similarities.

MIRROR FORMULAR
1. An object placed 15cm from a convex lens is magnified two times. Determine
the focal length of the lens. (3mk)

2. 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?

3. 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 (3mks)

4. 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?

5. An object is placed 30cm in front of a concave lens of focal length 20cm.

determine the magnification of the image produced. 4mks
6. 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.

7. An object is placed 16cm from a converging lens of focal length 12cm. Find.
(i) Position of image.
(iii) Magnification of the image.

8. Calculate the power of a lens whose focal length is given as 10cm.

9. A real image, half the size of the object is formed by a lens. If the distance
between the objects and the image is 450mm. Determine the focal length of
the objects. (3mks)

10. A object of height 10.5cm stands before a diverging lens of focal length 20cm
and a distance of10cm from the lens. Determine.
FORM4 THIN LENSES Pg8
 i) Image distance
ii) Height of the image
iii) Magnification

11. A lens forms a clear image on a screen. When the distance between the screen
and the object is 80cm, the image is 3 times the size of the object.
i) Explain the type of lens used. (2 mk)
ii) Determine the distance of the image from the lens. (3mk)
iii) Determine the focal length of the lens. (2mk)

12. A lens forms a focused image on a screen when the distance between the object
and the screen is 100 cm. The size of the image is thrice that of the object.
i) What kind of lens was used? Give a reason. (2mk)
ii) Determine the distance of the image from the lens. (3mk)
iii) Determine the power of the lens. (3mk)

13. 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 (5mk)

14. A lens has focal length of 12.5cm. Determine its power. (2mk)

15. A convex lens forms an image five times the size of the object on a screen. If
the distance between the object and the screen is 120cm, determine the focal
length of the lens. (3mk)

16. 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. (4mks)

17. 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 shows the experimental
set up when there is no parallax between the pin and the image.
Eye

Pin Image

20cm

Lens

Plane mirror

(i) Determine the focal length of the lens.

(ii) Explain how you arrive at your answer. (3mks)

FORM4 THIN LENSES Pg9

 18. The graph below shows the variation of 1/Vand 1/U in an experiment to
determine the focal length of the lens. Determine the focal length.

0.08
0.06
0.04
0.02

0.02 0.04 0.06 0.08

19. The graph below represents 1/V against1/U for an object paced in front of a
concave mirror.
0.05
0.04
0.03

0.02
0.01

0.01 0.02 0.03 0.04 0.05

From the graph determine the focal length of the lensand its power ? (4mk)
20. The graph below shows the relationship between (1/U) and (1/V) for an object
paced in front of a convex lens. From the graph, determine the focal length of
the lens.

25

20

15

10

5 10 15 20 25
21. The graph below shows the relationship between (1/U) and (1/V)for converging
lens where u and v are the object and image distances respectively.

2
1 x 10-1(cm-1)

1
u

FORM4 THIN LENSES Pg10

 0 1 2
1 x 10-1(cm-1)
v
From the graph, determine the focal length, f, of the lens. (5mks)
22. The graph below is a plot of image distance against the object for a concave
lens

16
14
V (cm) 12
10
8
6
4
2

2 4 6 8 10 12 14 16 18

U (cm)
From the graph determine the focal length of the concave lens. (3mk)
23. 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.
UV(cm2)

1600
1500

1400
1300
1200
1100
70
1000 72 74 76 78 80

U +V (cm)

a. Show that the slope of the graph is equal to the focal length (2 mk)
b. Determine the focal length of the lens from the graph. (2 mk)

FORM4 THIN LENSES Pg11

 24. In an experiment using a convex lens a graph of image distance V against the
magnification m was drawn as shown, from the equation v/f =m+1.

90

80
Image distance (V) cm
70
60

50
40
30

20

10

0 1 2 3 4 5
From the graph determine. Magnification (m)
(i) The slope S. (3mks)
(ii) The y-intercept (V-intercept), C (1mk)
S+C
(iii)Calculate the value of constant n given that n= 2 (2mk)
(iv)What is the physical significance of the value n?

25. The graph below 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
Magnification(m)

6
5

4
3
2
1
--021 10 20 30 40 50

V (cm)

FORM4 THIN LENSES Pg12

 1 1 1
= +
a) Given that the mirror formula is f u v , write down the equation of the graph.
(3 mks
b) Determine the object distance when m =1.0 (2 mks
c) Determine the focal length of the lens (3 mks)

26. The table below shows the object and the corresponding image distances in an
experiment with a convex lens.
Object distance U cm 80 33 26.5 22.5 20
Image distance V cm 20 33 40.0 56 72
Magnification M
(i) Complete the table giving your answers to 3 d.p. (3mks)
(ii) Plot a graph of linear magnification M against image distance V. (4mks)
(i) Given that the linear magnification is related to the image distance by the
V
formula: f = M +1 Determine the focal length f of the lens. (4mks)
iv) Determine the image distance when the magnification is 1. (2mks)

27. The table below shows the object distance, U and the corresponding image
distance, V for an object placed
U (cm) 20 25 30 35 40 45
V (cm) 60.0 37.5 30.0 26.3 24.0 22.5
1
u (cm-1)
1 1
V (cm (i)
) Complete the table and plot a graph of
-1 V
1
against u (7mks)
Determine the focal length of the lens. (2mks)

28. In a experiment to determine the focal length of a lens, the results in table 1
were obtained.

U (cm) 12.5 16.0 18.0 24.0 30.0 40.0

V (cm) 50.0 27.0 22.5 17.0 15.0 13.0

(i) Plot a graph of V (y-axis) against U (x-axis). (5 mks)

(ii) From your graph, determine the focal length of the lens. (3 mks)

FORM4 THIN LENSES Pg13