Mirrors Examples: 46 Problems with Answers

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

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

Concept Recap

Mirrors are reflective surfaces that form images by reflection. Physics courses usually study plane mirrors and curved mirrors such as concave and convex mirrors.

A mirror sends light back in a predictable way, so your eye traces the rays and sees an image.

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

Common stuck point: Students often know a formula related to mirrors 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 concave mirror has

f=15\text{ cm}

and the object is at

d_o = 45\text{ cm}

. Find

d_i

and the magnification.

Answer

d_{i} = 22.5 cm, m = - 0.5

First step

1/d_i = 1/15 - 1/45 = 3/45 - 1/45 = 2/45

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Example 2

medium

A makeup mirror is concave with

f = 20\text{ cm}

. To get a

2\times

upright image, where must the face be placed?

Example 3

medium

A concave mirror's image is half the size of the object and inverted, with the object at

d_o = 60\text{ cm}

. Find

f

Example 4

hard

An object stands

15\text{ cm}

from a concave mirror with

f=10\text{ cm}

, then moves to

25\text{ cm}

. Find the change in image distance.

Example 5

hard

A concave mirror has

f=12\text{ cm}

. An object is placed at

d_o=18\text{ cm}

then moved a small

\Delta d_o = 0.2\text{ cm}

closer. Use

d_i = f d_o/(d_o - f)

to estimate

\Delta d_i

Example 6

challenge

Two plane mirrors meet at a

60^\circ

angle, like a kaleidoscope corner. How many images of a single object are produced? (Use

N = 360^\circ/\theta - 1

Practice Problems

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

Example 1

easy

A concave mirror has focal length

f = 10 \text{ cm}

. An object is at

d_o = 30 \text{ cm}

. Find the image distance.

Concave mirror: f = 10 cm, d_o = 30 cm → find d_i

Example 2

easy

A flat (plane) mirror forms an image of an object 2 m in front of it. How far behind the mirror is the image?

Example 3

easy

Is the image in a flat mirror real or virtual?

Example 4

easy

A convex mirror always forms what type of image for a real object?

Example 5

easy

In the mirror sign convention used here, a real image has what sign of image distance

d_i

Example 6

easy

A concave mirror has radius of curvature

R = 20 \text{ cm}

. Find its focal length.

Example 7

easy

An object is placed exactly at the focal point of a concave mirror. Where does the image form?

Example 8

easy

Light from a distant star hits a concave mirror with

f = 50 \text{ cm}

. Where does the image form?

Concave mirror: f = 50 cm, distant object → d_i = f

Example 9

medium

A concave mirror (

f=10 \text{ cm}

) has an object at

d_o = 15 \text{ cm}

. Find the image distance and state if it is real or virtual.

Concave mirror: f

Example 10

medium

A concave mirror (

f=10 \text{ cm}

) has an object at

d_o = 5 \text{ cm}

(inside the focal point). Find

d_i

and the image type.

Concave mirror: f

Example 11

medium

A convex mirror has

f = -15 \text{ cm}

. An object is at

d_o = 30 \text{ cm}

. Find the image distance.

Example 12

medium

A concave mirror (

f=12 \text{ cm}

) forms an image at

d_i = 24 \text{ cm}

. Find the object distance.

Concave mirror: f

Example 13

medium

A concave mirror (

f=10 \text{ cm}

) has an object at

d_o=20 \text{ cm}

. Find the magnification.

Concave mirror: f

Example 14

medium

A 4 cm tall object stands before a concave mirror, giving

d_o = 30 \text{ cm}

and

d_i = 15 \text{ cm}

. Find the image height.

Concave mirror: d_o

Example 15

challenge

A concave mirror produces an image twice as tall and inverted, with the object at

d_o = 15 \text{ cm}

. Find the focal length.

Concave mirror: d_o

Example 16

challenge

An object 24 cm from a concave mirror produces a real image at 12 cm. The object then moves to 8 cm. Find the new image distance and type.

Example 17

challenge

A convex mirror (

f=-20 \text{ cm}

) shows an image one-third the object's height. Find the object distance.

Example 18

medium

A concave mirror (

f=8 \text{ cm}

) has an object at

d_o = 24 \text{ cm}

. Find the image distance.

Concave mirror: f

Example 19

medium

A convex mirror (

f=-10 \text{ cm}

) has an object at

d_o = 10 \text{ cm}

. Find the image distance.

Example 20

medium

A concave mirror has

f=15 \text{ cm}

and an object at

d_o=10 \text{ cm}

. Find the magnification.

Concave mirror: f

Example 21

easy

A concave mirror has radius of curvature

R = 40\text{ cm}

. Find its focal length.

Example 22

easy

A concave mirror has

f = 20\text{ cm}

. An object sits at

d_o = 60\text{ cm}

. Find

d_i

Example 23

easy

A concave mirror with

f = 10\text{ cm}

has an object at

d_o = 40\text{ cm}

, image at

d_i = 13.3\text{ cm}

. Find the magnification.

Example 24

easy

A concave mirror has

f = 5\text{ cm}

and the object is at

d_o = 10\text{ cm}

. Find

d_i

Example 25

easy

An object stands

1.5\text{ m}

in front of a plane mirror. What is the distance between the object and its image?

Example 26

medium

A concave mirror has

f = 8\text{ cm}

. To form an image at

d_i = 24\text{ cm}

, where must the object sit?

Example 27

medium

A convex mirror has

f = -20\text{ cm}

and the object is at

d_o = 40\text{ cm}

. Find

d_i

and state if the image is real or virtual.

Example 28

medium

A concave mirror (

f = 10\text{ cm}

) gives a virtual image at

d_i = -20\text{ cm}

. Where is the object?

Example 29

medium

5\text{ cm}

tall candle sits

30\text{ cm}

from a concave mirror with

f=10\text{ cm}

. Find the image height.

Example 30

medium

A convex mirror has

R = 30\text{ cm}

. Find its focal length (with sign).

Example 31

medium

2\text{ cm}

tall object is in front of a convex mirror with

f=-12\text{ cm}

, at

d_o = 24\text{ cm}

. Find the image height.

Example 32

medium

Where must an object sit in front of a concave mirror with

f=10\text{ cm}

to produce an image at

d_i = -20\text{ cm}

(virtual)?

Example 33

medium

A concave mirror has

f = 20\text{ cm}

. The object distance is twice the focal length. State the image type and magnification.

Example 34

hard

A concave mirror with

f=15\text{ cm}

forms an image

5\text{ cm}

tall from a

3\text{ cm}

tall object. Find the object distance, assuming the image is inverted and real.

Example 35

hard

A concave mirror produces a real image

36\text{ cm}

from the mirror when the object is

12\text{ cm}

from the mirror. Find

f

Example 36

hard

A convex mirror produces a virtual image

\tfrac{1}{4}

the height of the object placed

60\text{ cm}

from the mirror. Find

f

Example 37

hard

1.7\text{ m}

tall person stands

3\text{ m}

from a plane mirror. What is the minimum mirror height that lets them see themselves head to toe? (Assume eyes near the top of the head.)

Example 38

hard

A concave mirror gives

|m|=3

for an object at

d_o=8\text{ cm}

. Find both possible focal lengths (real-image and virtual-image cases).

Example 39

challenge

A telescope uses a concave primary mirror with

f = 2.0\text{ m}

. The Moon (

d_o \approx \infty

) has angular size

0.0093\text{ rad}

. Find the size of the lunar image at the focal plane.

Example 40

challenge

A convex security mirror (

f = -25\text{ cm}

) shows a shoplifter's image

\tfrac{1}{6}

the actual height. How far away is the shoplifter?

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Related Concepts

Reflection Ray Diagram Image Formation

Background Knowledge

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

reflection