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physics Physics For High Schools (KS4)
 
Solved problems for the chapter:
 

Thin Converging and Diverging Lenses

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Optical Imaging - Lenses
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Optical Imaging - Mirrors
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:thin_converging_and_diverging_lenses/3539/


Example 1.

An object is placed at a distance of 30 cm in front of a lens. The image of the object is at a distance of 60 cm on the other side of the lens.

  • What type is the lens and what is its focal length?

  • What is the magnification of the lens?

  • What is the nature of the image?

    
Example 2.

An object is placed at a distance of 30 cm in front of a lens. The image of the object is at a distance of 60 cm on the same side of the lens as the object.

  • What type is the lens and what is its focal length?

  • What is the magnification of the lens?

  • What is the nature of the image?

    
3.

A converging lens has a focal length of 15 cm. The lens forms a real image of an object at a distance of 40 cm.

  • What is the object distance?

  • What is the magnification of the lens?

    
4.

A converging lens has a focal length of 30 cm. An object is placed at a distance of 10 cm in front of the lens. The lens forms a real image of an object at a distance of 40 cm.

  • What is the distance of the image?

  • What is the magnification of the lens?

  • What is the nature of the image?

    
5.

An object of height 3 cm is placed in front of a lens. The distance of the object to the lens is 30 cm. The image formed is upright and 4 cm high.

  • What is the distance of the image?

  • What is the nature of the image?

  • What type is the lens?

    
6.

An image that is 6 times magnified is to be created using a converging lens of focal length 30 cm.

Where should we place the object, where will the picture be and what will the picture be like?

  • Where should the object be placed?

  • Where will the image be?

  • What is the nature of the image?

    
7.

The distance between the object and the screen where the image is to be displayed is 6 meters. Where do we need to place the lens with a focal length of 40 cm to make the image on the screen sharp and magnified? What is the magnification?

    
8.

A lens has a focal length of 20 cm. Behind the lens is a screen at a distance of 6 m.

  • Where should the object be placed in order to receive the image on the screen?

  • What is the magnification of the lens?

    

9.

A concave lens has a focal length of 20 cm. An object stands at a distance of 30 cm from the lens.

  • Where is the image of the object?

  • What is the magnification of the lens?

  • What is the nature of the image?

    
10.

An object is placed at a distance of 20 cm from a diverging lens. The image produced is reduced 3 times. What is the focal length of the lens?

    
11.

An object stands 30 cm in front of a diverging lens and its virtual image is at a distance of 20 cm from the lens. What is the focal length of the lens?

    
12.

An object stands at a distance of 35 cm in front of a converging lens. If we move the object away by 6.2 cm, its real image approaches the lens by 4.4 cm. What is the focal length of the lens?

    
13.

The reflector gives a beam of parallel rays. This beam is directed through a converging lens along the optical axis. What happens to the light rays on the other side of the lens?

Explain the optical axis, the focal length, and the focal length of the lens?

    
14.

Explain how a movie projector works! How is the image formed?

    
15.

A lighted candle is placed in front of a converging lens at a distance twice the focal length of the lens. Where is the image formed and what is its nature?

    
16.

A converging lens has a focal length of 6 cm. A 2 cm high object is placed at a distance of 4 cm from the lens. Describe how the image is formed and the nature of the image.

    
17.

On the same side of a converging lens are the object O and its image I, as shown in the figure below. Where is the lens and where is the focal point?


    
18.

A beam of light is directed at a diverging lens in the direction of the optical axis. What kind of beam is obtained on the other side of the lens?

    

19.

A concave mirror is 6 m away from the screen. An object is placed half-way between the screen and the mirror.

  • What should be the radius of the concave mirror for the image on the screen to be sharp?

  • What will be the magnification?


    
20.

How does the distance of an image from the vertex of a concave mirror change if we change the distance of the object? The focal length of the mirror is 20 cm.

    
21.

A concave mirror is made of a ball cap with a radius of 60 cm. An object 4 cm high is placed at a distance of 40 cm in front of the mirror. Where and what will be its image?

    
22.

A canvas is placed at a distance of 4 m in front of a concave mirror. We want to project the object on the screen.

  • Where do we need to place the screen to obtain an image that is four times the size of the object?

  • What should be the focal length of the mirror?


    
23.

A dentist uses a concave mirror with a focal length of 2 cm to examine teeth. In the mirror, he sees a tooth as an upright and three-times magnified image.

  • At what distance from the tooth does the dentist place the mirror?

  • Where is the image of the tooth?


    
24.

The focal length of a concave mirror is 12 cm. Where do we place the object so that:

  • the image will be upright and magnified three times?

  • the image will be inverted and magnified three times?

    
25.

An object is placed in front of a concave mirror at a distance of 16 cm. A virtual image appears at a distance of 40 cm behind the mirror. What is the radius of the mirror?

    
26.

An object is placed at a distance of 10 cm in front of a convex mirror. Plot the graph of the distance of the image against the focal length of the mirror. Describe the image of the object.

    
27.

The radius of a convex mirror is 60 cm. An object is placed 15 cm from the mirror.

  • Where is the image formed?

  • What is the magnification?

    
28.

An object, 10 cm high, is placed in front of a convex mirror of radius 60 cm. The image is 2 cm high.

  • Where is the object placed?

  • Where is the image formed?

    

29.

A silver-plated glass ball has a radius of 20 cm. A lamp is placed at a distance of 50 cm from the centre of the ball. Where is the image of the lamp?

    
30.

An object stands at a distance of 24 cm in front of a concave mirror. Its image is reduced 6 times.

  • What is the image distance and the focal length of the mirror?

  • If the mirror is replaced with a convex mirror, what is the image distance and the focal length of the mirror?

  • What is the difference between the images produced by both mirrors?

    
31.

A candle is placed in front of a converging lens at a distance greater than the focal length of the lens. The candle stands on the optical axis of the lens. Describe all the rays from the object that form the image. What is the nature of the image produced?

    
32.

A thin converging lens is used to produce a real image of an object. Which statement about the real image is always correct?


  • It is nearer to the lens than the object.


  • It is on the opposite side of the lens to the object.


  • It is the same size as the object.


  • It is upright.

    
33.

A student passes parallel rays of light through four different converging lenses. He measures the distance x and the distance y for each experiment.




Which lens has the longest focal length?


 
x/
y/
 
A
4.6
2.0
 
B
5.1
3.1
 
C
5.9
2.3
 
D
6.1
2.4
 
    
34.

A thin converging lens in a camera produces a real image on a photo-sensitive surface, as shown. At which position is the image of the top of the object formed?


    
35.

The diagram shows part of a ray diagram that demonstrates the formation of a virtual image Y of object X by a converging lens.




One ray of light from X is shown approaching the lens. Which arrow shows the direction of this ray as it leaves the lens?


    
36.

An object O is placed at point P near to a thin converging lens. The diagram shows three rays from the top of O passing through the lens. Each point F is one focal length from the centre of the lens. Each point 2 F is two focal lengths from the centre of the lens.




The object O is moved to point Q on the diagram. Which type of image is produced when the object O is at point Q?


  • inverted and the same size as the object


  • inverted and enlarged


  • upright and the same size as the object


  • upright and enlarged

    
37.

The diagram shows two diverging rays of light passing through a lens and emerging parallel to each other. Which labelled distance is the focal length of the lens?


    
38.

Each point F is one focal length from the centre of the lens. Each point 2F is two focal lengths from the centre of the lens. Which diagram shows a converging lens being used as a magnifying glass?


    

39.

The diagram shows a partly completed scale drawing of an upright object placed in front of a thin converging lens of focal length .




What is the nature of the image formed by this lens?


  • diminished, inverted and closer to the lens than the object


  • diminished, upright and further from the lens than the object


  • enlarged, inverted and closer to the lens than the object


  • enlarged, inverted and further from the lens than the object

    
40.

A thin converging lens has a focal length . An object O is placed to the left of the lens, as shown.




Where is the image formed and how does its size compare to the object?


 
image position
image size
 
A
on the opposite side of the lens to the object
larger than the object
 
B
on the opposite side of the lens to the object
smaller than the object
 
C
on the same side of the lens as the object
larger than the object
 
D
on the same side of the lens as the object
smaller than the object
 
    
41.

What are the correct labels for the ray diagram?




 
object
image
principal
focus
 
A
W
X
Y
 
B
W
Z
Y
 
C
X
Y
Z
 
D
X
Z
W
 
    
42.

The diagram shows the action of a thin converging lens on two rays of light. The rays are from the top of an object O. An inverted image I is formed.




Which name is given to the distance RS?


  • principal axis


  • principal focus


  • focal length


  • real length

    
43.

A person uses a magnifying glass to look at a stamp. Which ray diagram shows a thin converging lens being used to do this?


    
44.

An object is placed in front of a converging lens. The lens has a focal length f. In which labelled position should the object be placed in order to produce a real image that is smaller than the object?


    
45.

A thin converging lens can produce both real and virtual images. Which row describes a real and a virtual image?


 
real image
virtual image
 
A
rays converge to form the image
image can be projected onto a screen
 
B
rays converge to form the image
image cannot be projected onto a screen
 
C
rays diverge to form the image
image can be projected onto a screen
 
D
rays diverge to form the image
image cannot be projected onto a screen