Practice Lenses in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

medium

Two thin lenses with powers

+3 \text{ D}

and

+2 \text{ D}

are placed in contact. Find the combined focal length.

Example 2

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=−10 cm, do=20 cm — find d_i and magnification

Example 3

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=25 cm, do=50 cm — find image distance

Example 4

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=5 cm, di=20 cm — find object distance

Example 5

easy

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

Example 6

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=15 cm — find object distance

Example 7

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=12 cm — find do and di

Example 8

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=12 cm, do=18 cm — find d_i and magnification

Example 9

medium

Two thin lenses in contact have powers

+4\,\text{D}

and

-1\,\text{D}

. Find the combined focal length.

Example 10

easy

What sign of

d_i

indicates a virtual image?

Example 11

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=5 D, do=0.10 m (inside f) — find di (virtual)

Example 12

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 13

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 14

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 = 10 cm — find d_i and real/virtual

Example 15

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 16

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

Example 17

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=20 cm) with intermediate object at 30 cm — final image at 60 cm

Example 18

easy

A converging lens with

f = 10\,\text{cm}

has an object at infinity. Where is the image?

Example 19

easy

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

Example 20

easy

In the lens sign convention here, a positive image distance

d_i

means the image is on which side?

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Refraction Ray Diagram Image Formation