Lenses Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Lenses.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Lenses are transparent optical devices that form images by refraction. A converging lens brings parallel rays together, while a diverging lens spreads them apart.

A lens bends light on purpose so an image can be focused or spread out.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Lenses starts by following rays or wavefronts through boundaries, materials, and image locations.

Common stuck point: Students often know a formula related to lenses but skip the recognition step: Am I tracking how light travels through space or materials, including boundary rules and image location when needed? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I tracking how light travels through space or materials, including boundary rules and image location when needed?

Worked Examples

Example 1

medium

A converging lens with

f = 10\,\text{cm}

produces an image of a

4\,\text{cm}

object at

d_o = 30\,\text{cm}

. Find the image height.

Converging lens: f=10 cm, do=30 cm, ho=4 cm — find image height

Answer

h_{i} = - 2 cm

First step

1/d_i = 1/10 - 1/30 = 2/30 = 1/15

, so

d_i = 15\,\text{cm}

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Example 2

medium

A camera lens with

f = 50\,\text{mm}

focuses on a subject

2\,\text{m}

away. Find the image distance (sensor position) from the lens.

Example 3

hard

A converging lens with

f = 10\,\text{cm}

has an object

40\,\text{cm}

in front of it. A second identical lens sits

20\,\text{cm}

behind the first. Find the final image distance from the second lens.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A converging lens has

f = 20 \text{ cm}

. An object is at

d_o = 60 \text{ cm}

. Find the image distance.

Converging lens: object at 60 cm, f = 20 cm — find d_i

Example 2

easy

Does a converging lens bring parallel rays together or spread them apart?

Example 3

easy

What is the sign of the focal length of a diverging lens?

Example 4

easy

Lenses form images by which process?

Example 5

easy

A converging lens (

f=15 \text{ cm}

) has a distant object (

d_o \to \infty

). Where is the image?

Example 6

easy

In the lens sign convention here, a positive image distance

d_i

means the image is on which side?

Example 7

easy

A converging lens has power

P = 4 \text{ D}

(diopters). Find its focal length in meters.

Example 8

easy

A diverging lens always forms what kind of image for a real object?

Example 9

medium

A converging lens (

f=10 \text{ cm}

) has an object at

d_o = 15 \text{ cm}

. Find

d_i

and state real or virtual.

Converging lens: object at 15 cm, f

Example 10

medium

A converging lens (

f=10 \text{ cm}

) has an object at

d_o = 5 \text{ cm}

(inside the focus). Find

d_i

and the image type.

Converging lens as magnifier: object inside f at 5 cm — virtual image at 10 cm

Example 11

medium

A diverging lens (

f=-20 \text{ cm}

) has an object at

d_o = 30 \text{ cm}

. Find the image distance.

Diverging lens: object at 30 cm, f

Example 12

medium

A converging lens (

f=10 \text{ cm}

) has an object at

d_o = 20 \text{ cm}

. Find the magnification.

Object at 2f: converging lens f

Example 13

medium

A converging lens (

f=12 \text{ cm}

) projects an image onto a screen at

d_i = 36 \text{ cm}

. Find the object distance.

Projector setup: f

Example 14

medium

Two thin lenses with powers

+3 \text{ D}

and

+2 \text{ D}

are placed in contact. Find the combined focal length.

Example 15

challenge

A converging lens forms a real image twice the object's size on a screen. The lens has

f = 15 \text{ cm}

. Find the object distance.

Real image 2× object height: f

Example 16

challenge

An object is 30 cm from a converging lens (

f_1=10 \text{ cm}

). A second lens (

f_2=20 \text{ cm}

) sits 25 cm beyond the first. Find the final image distance from the second lens.

Example 17

challenge

A diverging lens (

f=-15 \text{ cm}

) forms an image one-fourth the object height. Find the object distance.

Diverging lens: image one-quarter object height, f

Example 18

medium

A converging lens (

f=8 \text{ cm}

) has an object at

d_o = 24 \text{ cm}

. Find the image distance.

Converging lens: f

Example 19

medium

A diverging lens (

f=-10 \text{ cm}

) has an object at

d_o = 10 \text{ cm}

. Find the image distance.

Diverging lens: f

Example 20

medium

A converging lens has power

P = 5 \text{ D}

. An object is at

d_o = 0.10 \text{ m}

. Find the image distance in meters.

Converging lens: P

Example 21

easy

A converging lens has

f = 25\,\text{cm}

. An object sits at

d_o = 50\,\text{cm}

. Find the image distance.

Object at 2f: f

Example 22

easy

A lens has power

P = -2\,\text{D}

. Find its focal length in meters and identify the lens type.

Example 23

easy

A converging lens with

f = 10\,\text{cm}

has an object at infinity. Where is the image?

Example 24

easy

A converging lens has power

P = 2\,\text{D}

. Find

f

in cm.

Example 25

easy

A converging lens forms an image at

d_i = 40\,\text{cm}

from an object at

d_o = 40\,\text{cm}

. Find

f

Example 26

medium

A converging lens (

f = 12\,\text{cm}

) has an object at

d_o = 18\,\text{cm}

. Find

d_i

and the magnification.

Converging lens: f

Example 27

medium

A diverging lens (

f = -15\,\text{cm}

) has an object at

d_o = 15\,\text{cm}

. Find

d_i

Diverging lens: f

Example 28

medium

A converging lens with

f = 8\,\text{cm}

has an object at

d_o = 6\,\text{cm}

(inside the focal length). Find

d_i

and identify the image type.

Magnifying glass: f

Example 29

medium

A converging lens projects a real image of magnification

m = -3

onto a screen

60\,\text{cm}

from the lens. Find

f

Example 30

medium

Two thin lenses in contact have powers

+4\,\text{D}

and

-1\,\text{D}

. Find the combined focal length.

Example 31

medium

A converging lens with

f = 20\,\text{cm}

has an object at

d_o = 30\,\text{cm}

. Find the magnification.

Converging lens: f

Example 32

medium

A converging lens forms a real image

20\,\text{cm}

from the lens. The object is

30\,\text{cm}

from the lens. Find

f

Example 33

medium

A diverging lens (

f = -10\,\text{cm}

) has an object at

d_o = 20\,\text{cm}

. Find

d_i

and

m

Diverging lens: f

Example 34

medium

A converging lens has

f = 5\,\text{cm}

and forms an image at

d_i = 20\,\text{cm}

. Find

d_o

Converging lens: f

Example 35

hard

A converging lens forms a real image

4

times the object height on a screen. The lens has

f = 12\,\text{cm}

. Find

d_o

and

d_i

Real image 4× height: f

Example 36

hard

A diverging lens (

f = -20\,\text{cm}

) forms an image at half the object height. Find

d_o

Diverging lens: image half object height — find object distance

Example 37

hard

A converging lens has

f = 6\,\text{cm}

. Find the object distance that produces a real image at

d_i = 18\,\text{cm}

Converging lens: f

Example 38

hard

A lens of power

+5\,\text{D}

is combined in contact with a lens of power

-3\,\text{D}

. An object sits

30\,\text{cm}

in front of the combination. Find

d_i

Combined lens P

Example 39

hard

A converging lens with

f = 20\,\text{cm}

is used as a simple magnifier with the image at the near point

25\,\text{cm}

. Find the object distance.

Example 40

hard

A converging lens projects an image whose height is one-third the object's onto a screen. The lens has

f = 15\,\text{cm}

. Find

d_o

Converging lens: image 1/3 object height, f

Example 41

challenge

A converging lens with

f = 10\,\text{cm}

is used to image an object so the image-to-object distance is minimum. Find

d_o

and that minimum total distance.

Example 42

challenge

A two-lens system has lens 1 (

f_1 = 10\,\text{cm}

) and lens 2 (

f_2 = 20\,\text{cm}

) separated by

50\,\text{cm}

. An object sits

20\,\text{cm}

in front of lens 1. Find the final image distance from lens 2.

Two-lens system: lens 2 (f

Example 43

challenge

A microscope objective (

f_o = 0.8\,\text{cm}

) and eyepiece (

f_e = 2.5\,\text{cm}

) are separated by tube length

L = 16\,\text{cm}

. Find the total magnification with the final image at infinity. (Near point

= 25\,\text{cm}

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Related Concepts

Refraction Ray Diagram Image Formation

Background Knowledge

These ideas may be useful before you work through the harder examples.

refraction