Ray Diagram Examples in Physics

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

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

Concept Recap

A ray diagram is a drawing that uses a few principal rays to show how mirrors or lenses form images.

Instead of tracing every ray of light, you trace only the key rays that tell you where the image must be.

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

Common stuck point: Students often know a formula related to ray diagram 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

Sketch (describe) the ray diagram for an object at

d_o = 1.5f

from a converging lens. Where is the image and what kind?

Answer

d_i = 3f,\ \text{real, inverted, magnified } (m=-2)

First step

1/f = 1/(1.5f) + 1/d_i \Rightarrow 1/d_i = 1/f - 2/(3f) = 1/(3f)

, so

d_i = 3f

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Example 2

medium

A concave mirror has radius of curvature

R = 40\,\text{cm}

. Find

f

and locate the image for an object at

d_o = 60\,\text{cm}

Example 3

medium

A converging lens with

f=5\,\text{cm}

forms an image of a candle at

d_o=10\,\text{cm}

. Find

d_i

and

m

Example 4

medium

A converging lens with

f = 12\,\text{cm}

has an object at

d_o = 18\,\text{cm}

. Find

d_i

and

m

Example 5

hard

A two-lens system: lens 1 (

f_1 = 10\,\text{cm}

) followed by lens 2 (

f_2 = 15\,\text{cm}

) separated by

30\,\text{cm}

. Object at

20\,\text{cm}

in front of lens 1. Find the final image location relative to lens 2.

Example 6

hard

A concave mirror has

f = 15\,\text{cm}

; object at

d_o = 10\,\text{cm}

. Find

d_i

and describe the image.

Example 7

medium

Find

d_i

and

m

for a diverging lens with

f = -25\,\text{cm}

and an object at

d_o = 50\,\text{cm}

Example 8

hard

An object at

d_o = 8\,\text{cm}

in front of a converging lens produces an image

24\,\text{cm}

beyond on the opposite side. Find

f

Example 9

challenge

In a microscope, the objective (

f_o = 1.0\,\text{cm}

) has an object at

d_o = 1.2\,\text{cm}

. Find the image distance from the objective.

Example 10

challenge

In the same microscope, the intermediate image forms

0.5\,\text{cm}

inside the focal point of the eyepiece (

f_e = 5\,\text{cm}

). Find the final image distance from the eyepiece.

Practice Problems

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

Example 1

easy

In a ray diagram, a ray entering parallel to the axis of a converging lens leaves going through which point?

Example 2

easy

In a ray diagram for a converging lens, a ray through the center of the lens does what?

Example 3

easy

For a concave mirror, a ray coming in parallel to the axis reflects through which point?

Example 4

easy

In ray diagrams, how are rays drawn for a virtual image?

Example 5

easy

How many principal rays are typically enough to locate an image in a ray diagram?

Example 6

easy

For a converging lens, a ray passing through the near focal point emerges how?

Example 7

easy

A real image in a ray diagram forms where the actual outgoing rays do what?

Example 8

easy

On a plane mirror ray diagram, the image is located by reflecting rays and extending them where?

Example 9

medium

A converging lens (

f=10 \text{ cm}

) has an object at

d_o=20 \text{ cm}

(

=2f

). A ray diagram predicts the image is where, and what size?

Example 10

medium

Using a ray diagram for an object inside the focal length of a converging lens, what kind of image is predicted?

Example 11

medium

In a concave mirror ray diagram, the object is between the mirror and the focal point. What image results?

Example 12

medium

A diverging lens ray diagram is drawn for an object at any finite distance. What image always results?

Example 13

medium

Why does a ray diagram only need the principal rays rather than every ray of light?

Example 14

medium

In a concave mirror diagram, a ray that passes through the center of curvature

C

reflects how?

Example 15

challenge

An object 5 cm tall sits 30 cm from a converging lens with

f = 10 \text{ cm}

. Predict from a ray diagram the image distance and height.

Example 16

challenge

A concave mirror (

f=8 \text{ cm}

) has an object at

C

, the center of curvature (

d_o=16 \text{ cm}

). What does the ray diagram predict?

Example 17

challenge

A converging lens forms a real image on a screen. If you cover the top half of the lens, what happens to the image in the ray diagram?

Example 18

medium

For a converging lens, name the three principal rays used in a ray diagram.

Example 19

medium

A concave mirror diagram has the object beyond the center of curvature

C

. What image type results?

Example 20

medium

In a ray diagram, why must at least two principal rays come from the same point of the object?

Example 21

easy

In a ray diagram for a converging lens, name the three standard 'principal rays'.

Example 22

easy

A converging lens has

f=8\,\text{cm}

. An object sits at

d_o = 24\,\text{cm}

. Where does the image form?

Example 23

easy

For a plane mirror, the image of an object

30\,\text{cm}

in front of the mirror sits where?

Example 24

easy

For a concave mirror with

f = 10\,\text{cm}

and object at

25\,\text{cm}

, will the image be real or virtual?

Example 25

medium

For a converging lens with

f=6\,\text{cm}

, an object is placed

4\,\text{cm}

in front. Find

d_i

Example 26

medium

A diverging lens has

f = -10\,\text{cm}

. Object at

d_o = 15\,\text{cm}

. Find

d_i

and the image type.

Example 27

medium

A converging lens forms a real image

20\,\text{cm}

from the lens of a

5\,\text{cm}

-tall object whose image is

10\,\text{cm}

tall. Find the magnification and tell if it is upright or inverted.

Example 28

medium

For a convex mirror, an object is placed in front of it. What type of image always results?

Example 29

medium

A ray diagram shows two rays from the object intersecting

25\,\text{cm}

behind a lens. What does that intersection point represent?

Example 30

hard

In the same two-lens setup, find the total magnification.

Example 31

hard

Object at

d_o = f

in front of a converging lens. Where does the image form?

Example 32

hard

A convex mirror has

f = -20\,\text{cm}

(sign convention: negative). Object at

d_o = 30\,\text{cm}

. Find

d_i

and

m

Example 33

medium

In a ray diagram for a concave mirror, what is the special property of a ray that passes through the center of curvature C?

Example 34

easy

For a converging lens, the magnification of an object placed at

2f

is what?

Example 35

easy

For the eye, a converging lens forms an image where, relative to the lens?

Example 36

medium

An object of height

4\,\text{cm}

is placed

15\,\text{cm}

from a converging lens with

f = 10\,\text{cm}

. Find the image height.

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Related Concepts

Mirrors Lenses Image Formation

Background Knowledge

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

mirrorslenses