Image Formation Examples in Physics

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

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

Concept Recap

Image formation is the process by which reflected or refracted light creates an image that can be real or virtual, upright or inverted, and magnified or reduced.

Your eye or a screen sees an image based on where the outgoing rays meet or appear to meet.

Read the full concept explanation →

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: Image Formation starts by following rays or wavefronts through boundaries, materials, and image locations.

Common stuck point: Students often know a formula related to image formation 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 = 20 \text{ cm}

has an object at

d_o = 30 \text{ cm}

. Find

d_i

Answer

d_i = 60 \text{ cm}

First step

Thin lens:

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

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Example 2

medium

A concave mirror (

f=15 \text{ cm}

) has an object at

d_o=10 \text{ cm}

. Find

d_i

and

m

Example 3

medium

Using

f=-10

cm and

d_o=20

cm (above), find

m

and confirm the image type.

Example 4

hard

A converging lens with

f = 8 \text{ cm}

has an object 6 cm tall at

d_o = 24 \text{ cm}

. Describe the image fully.

Example 5

hard

A diverging lens forms a virtual image at

d_i=-12 \text{ cm}

when the object is at

d_o=24 \text{ cm}

. Find

f

and

m

Example 6

hard

A converging lens (

f=10

cm) forms an image with

|m|=4

. Find both possible object distances.

Example 7

hard

Why does a virtual image lack the ability to be projected, even though we still call it an image?

Example 8

challenge

Two converging lenses (each

f=10

cm) are 30 cm apart. An object sits 20 cm in front of lens 1. Find where the final image forms relative to lens 2.

Example 9

challenge

A concave mirror with

f=20

cm forms an image with

h_i = -5 \text{ cm}

when the object is 4 cm tall. Find

d_o

and

d_i

Practice Problems

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

Example 1

easy

An image with magnification

m = -2

is described how in size and orientation?

Example 2

easy

Can a virtual image be projected onto a screen?

Example 3

easy

An object 6 cm tall forms an image 3 cm tall and upright. Find the magnification.

Example 4

easy

A real image is always oriented how relative to the object for a single lens or mirror?

Example 5

easy

A virtual image from a single converging lens or mirror is oriented how?

Example 6

easy

An object and its image have

d_o = 20 \text{ cm}

and

d_i = 10 \text{ cm}

. Find the magnification.

Example 7

easy

|m| > 1

, is the image larger or smaller than the object?

Example 8

easy

Why are virtual images still considered genuine images even though they cannot be projected?

Example 9

medium

A lens forms an image with

d_o = 25 \text{ cm}

and

d_i = -50 \text{ cm}

. Find the magnification and describe the image.

Example 10

medium

A 10 cm object forms a 4 cm inverted image. The object distance is

d_o = 25 \text{ cm}

. Find the image distance.

Example 11

medium

A concave mirror (

f=10 \text{ cm}

) has an object at

d_o=40 \text{ cm}

. Describe the image fully (location, size, orientation, type).

Example 12

medium

An image is upright and the same size as the object. What is the magnification, and what optical element gives this for any object distance?

Example 13

medium

A lens gives

d_o = 30 \text{ cm}

d_i = 60 \text{ cm}

, object height 5 cm. Find the image height and orientation.

Example 14

medium

A real image forms at

d_i = 20 \text{ cm}

and is half the object's height. Find the object distance.

Example 15

challenge

A converging lens (

f=12 \text{ cm}

) has an object at

d_o=18 \text{ cm}

. Find the full image description including height for a 3 cm object.

Example 16

challenge

An object placed 10 cm from a lens gives an upright image 3 times as tall. Find the focal length.

Example 17

challenge

A concave mirror gives an image at

d_i = -30 \text{ cm}

(virtual) when the object is at

d_o = 12 \text{ cm}

. Find the focal length and magnification.

Example 18

medium

An object 8 cm tall forms an image 2 cm tall and inverted. Find the magnification.

Example 19

medium

A lens gives

d_o=15 \text{ cm}

and

d_i=-30 \text{ cm}

. Describe the image type and orientation.

Example 20

medium

An object forms a real image 3 times its height at

d_i = 60 \text{ cm}

. Find the object distance.

Example 21

easy

An object 4 cm tall produces a 6 cm tall inverted image. Find

m

Example 22

easy

d_o = 30 \text{ cm}

and

d_i = 15 \text{ cm}

. Find

m

Example 23

easy

A 5 cm object has

m = -0.4

. Find the image height.

Example 24

easy

d_o = 40 \text{ cm}

d_i = -20 \text{ cm}

. Find

m

and describe the image.

Example 25

medium

For the lens above (

f=20

cm,

d_o=30

cm,

d_i=60

cm), find

m

Example 26

medium

An 8 cm object forms a 24 cm inverted image at

d_i = 90

cm. Find

d_o

Example 27

medium

d_o = 12 \text{ cm}

d_i = 24 \text{ cm}

, object height

h_o = 4 \text{ cm}

. Find

h_i

Example 28

medium

A real image is

1/3

the object's height and at

d_i = 20

cm. Find

d_o

Example 29

medium

A diverging lens has

f = -10 \text{ cm}

. An object sits at

d_o = 20 \text{ cm}

. Find

d_i

Example 30

medium

A convex (diverging) mirror with

f = -20 \text{ cm}

shows an object at

d_o = 30 \text{ cm}

. Find

d_i

Example 31

medium

A lens forms a real image of the same height as the object at

d_i = 30 \text{ cm}

. Find

d_o

and

f

Example 32

hard

A concave mirror with

f=10 \text{ cm}

has an object at

d_o=8 \text{ cm}

. Find

d_i

and

m

Example 33

hard

An upright image is twice the object's height. The object is at

d_o = 15 \text{ cm}

. Find

d_i

and the focal length (assuming a single lens or mirror).

Example 34

hard

An object is at

d_o = 2f

in front of a converging lens. Find

d_i

in terms of

f

, and find

m

Example 35

hard

A 2 cm coin is viewed through a magnifying glass (

f=5

cm) held 4 cm above. Find the apparent height of the image.

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Related Concepts

Ray Diagram Mirrors Lenses

Background Knowledge

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

ray diagrammirrorslenses