Speed of Light Examples: 47 Problems with Answers

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

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

Concept Recap

The speed of light is the speed at which electromagnetic waves travel in a vacuum. It is one of the most important constants in physics.

Light moves incredibly fast, but not infinitely fast.

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: Speed of Light starts by following rays or wavefronts through boundaries, materials, and image locations.

Common stuck point: Students often know a formula related to speed of light 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

Light enters water (

n = 1.33

) from air. Find the speed of light in water and the ratio

v/c

Answer

v \approx 2.26 \times 10^{8} m/s, v / c \approx 0.752

First step

Use

v = c/n

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Example 2

medium

A pulse takes

1.2\times10^{-8}\text{ s}

to cross a

3.0\text{ m}

glass slab. Find

n

Example 3

hard

A pulse travels 120 m in vacuum and then 80 m through water (

n = 1.33

). Find the total time.

Example 4

hard

A radar pulse hits an airplane

30\text{ km}

away. Find the round-trip time in vacuum (treat air as vacuum).

Example 5

challenge

Light from a star moving away at

0.1c

arrives at Earth. What speed does an Earth observer measure for the light?

Practice Problems

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

Example 1

easy

Light travels through a vacuum. What is its speed?

Example 2

easy

A radio wave in vacuum has frequency

f = 1.0 \times 10^8 \text{ Hz}

. Find its wavelength.

Example 3

easy

How long does light take to travel

3.0 \times 10^8 \text{ m}

in vacuum?

Example 4

easy

Is the speed of light in vacuum the same for all observers?

Example 5

easy

Compare the speed of light to the speed of sound (about

340 \text{ m/s}

). Which is faster?

Example 6

easy

Green light has wavelength

\lambda = 5.0 \times 10^{-7} \text{ m}

in vacuum. Find its frequency.

Example 7

easy

Light from the Sun takes about

500 \text{ s}

to reach Earth. Roughly how far is the Sun?

Example 8

easy

In vacuum, do red light and blue light travel at the same speed?

Example 9

medium

Light travels through glass with refractive index

n = 1.5

. Find its speed in the glass.

Light slows from c to v = c/n in glass

Example 10

medium

Light moves at

2.25 \times 10^8 \text{ m/s}

in water. Find the refractive index of water.

Example 11

medium

A wavelength in vacuum is

\lambda_0 = 600 \text{ nm}

. In glass (

n=1.5

) the frequency is unchanged. Find the wavelength in glass.

Example 12

medium

How far does light travel in vacuum in one nanosecond (

1.0 \times 10^{-9} \text{ s}

Example 13

medium

A laser pulse travels 1.2 km down an optical fiber where light speed is

2.0 \times 10^8 \text{ m/s}

. Find the travel time.

Example 14

medium

A star is 4.0 light-years away. Express that distance in meters (1 yr

\approx 3.15\times10^7 \text{ s}

Example 15

medium

Microwaves in vacuum have

f = 2.4 \times 10^9 \text{ Hz}

. Find their wavelength.

Example 16

challenge

Light goes from water (

n=1.33

) into glass (

n=1.5

). By what factor does its speed change?

Example 17

challenge

An observer measures light from a fast-moving spaceship's headlight. The ship moves at

0.5c

toward the observer. What speed does the observer measure for the light?

Example 18

challenge

A pulse must travel 300 m through air (

n\approx1

) then 200 m through glass (

n=1.5

). Find the total time. Use

c=3.0\times10^8 \text{ m/s}

Example 19

medium

A pulse of light reflects off a mirror

4.5 \text{ m}

away and returns. Find the round-trip time in vacuum.

Example 20

medium

Light enters a diamond (

n=2.42

). Find its speed in the diamond.

Example 21

easy

A laser pulse travels through vacuum for

5.0\times10^{-9}\text{ s}

. How far does it go? Use

c = 3.00\times10^8\text{ m/s}

Example 22

easy

Red light has frequency

4.6\times10^{14}\text{ Hz}

. Find its wavelength in vacuum (use

c = 3.0\times10^8

Example 23

easy

How long does light take to travel

1.0\text{ km}

in vacuum?

Example 24

easy

Light from the Moon takes about

1.28\text{ s}

to reach Earth. Find the Earth-Moon distance.

Example 25

easy

Sunlight reaches Earth in about

500\text{ s}

. Express the Sun's distance in km.

Example 26

easy

FM radio broadcasts at

f = 100\text{ MHz}

. Find the wavelength in vacuum.

Example 27

medium

Light enters glycerin where it travels at

2.04\times10^8\text{ m/s}

. Find the refractive index.

Example 28

medium

Blue light has vacuum wavelength

\lambda_0 = 450\text{ nm}

. Find its wavelength in glass with

n = 1.52

Example 29

medium

A pulse must travel

500\text{ m}

through a fiber with

n = 1.45

. Find the travel time.

Example 30

medium

A light-year (ly) is the distance light travels in one year (

\approx 3.15\times10^7\text{ s}

). Find the meters in 1 ly.

Example 31

medium

How long does a signal take to travel

36000\text{ km}

to a geostationary satellite (one-way)?

Example 32

medium

A green laser has vacuum wavelength

532\text{ nm}

. Find its frequency.

Example 33

medium

A signal travels

1.5\text{ AU}

between Earth and Mars (closest approach). Time in minutes?

Example 34

medium

Compare light speed in vacuum vs. diamond (

n = 2.42

). Find the speed ratio.

Example 35

medium

A radio wave has

\lambda = 6.0\text{ m}

in vacuum. Find its frequency.

Example 36

hard

Light enters glass (

n = 1.5

) from air with vacuum wavelength

600\text{ nm}

. Find the photon energy in joules (

h = 6.63\times10^{-34}\text{ J s}

Example 37

hard

Earth's circumference is about

4.0\times10^7\text{ m}

. How many times can light circle Earth per second (in vacuum)?

Example 38

hard

Light slowed to

v = 1.5\times10^8\text{ m/s}

in a medium has the same vacuum wavelength of

600\text{ nm}

. Find the wavelength in the medium.

Example 39

hard

A photon source emits

2.0\times10^{18}

photons/s of green light (

\lambda = 500\text{ nm}

). Find the total power. (

h = 6.63\times10^{-34}\text{ J s}

Example 40

hard

A light pulse spends

1\text{ ns}

in a

0.2\text{ m}

block. Find its refractive index.

Example 41

challenge

A laser of vacuum wavelength

600\text{ nm}

enters a slab of index

n=1.5

and thickness

L=3\text{ mm}

. How many extra wavelengths does it fit in the slab compared to vacuum?

Example 42

challenge

A round-trip light-pulse experiment over

2L = 600\text{ m}

in air gives

t = 2.00\times10^{-6}\text{ s}

. From this, estimate

c

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Related Concepts

Electromagnetic Waves Wave Speed Visible Light Special Relativity

Background Knowledge

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

electromagnetic waveswave speed