Total Internal Reflection Examples: 46 Problems with Answers

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

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

Concept Recap

Total internal reflection happens when light traveling in a higher-index medium hits a boundary to a lower-index medium at an angle greater than the critical.

At a steep enough angle, light gets trapped and bounces inside the material.

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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: Total Internal Reflection starts by following rays or wavefronts through boundaries, materials, and image locations.

Common stuck point: Students often know a formula related to total internal reflection 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 glass core (

n_1 = 1.50

) is surrounded by cladding (

n_2 = 1.45

). Find the critical angle at the core-cladding boundary.

Answer

θ_{c} \approx {75.2}^{\circ}

First step

\sin\theta_c = 1.45/1.50 = 0.9667

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Example 2

medium

A right-angle prism (

n=1.52

) is used as a periscope element. Light enters the long face normally and hits the hypotenuse at

45^\circ

. Does it TIR off the hypotenuse?

Example 3

medium

Light travels from glass (

n=1.52

) into water (

n=1.33

). Find the critical angle.

Example 4

medium

Light is incident on a glass-air boundary (

n_{\text{glass}}=1.50

) at

35^\circ

. Find the refracted angle in air.

Example 5

hard

A fiber has core index

n_1 = 1.50

and cladding

n_2 = 1.46

. Find the maximum acceptance angle

\theta_a

in air for a ray that will be guided by TIR.

Example 6

hard

A cubic glass block (

n=1.50

) sits in air. A horizontal laser enters one vertical face at

20^\circ

from the normal. Find the angle of refraction inside and check whether the ray TIRs off the top face.

Example 7

hard

Find the critical angle when light passes from a material with

n_1 = 1.65

into another with

n_2 = 1.33

Example 8

medium

Show that the critical angle for crown glass (

n=1.52

) in air is about

41.1^\circ

Example 9

medium

Find the critical angle for light passing from a glass with

n_1 = 1.75

into air.

Example 10

challenge

A point source sits

1.0\,\text{m}

below the surface of a calm lake (

n=1.33

). Find the radius of the bright circle of light that escapes into the air above.

Example 11

challenge

A graded-index fiber has core

n_1 = 1.48

and cladding

n_2 = 1.46

. Find the numerical aperture (NA) and the maximum acceptance half-angle in air.

Practice Problems

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

Example 1

easy

For total internal reflection to occur, light must travel from a medium with which index toward which?

Example 2

easy

Find the critical angle for light going from glass (

n_1=1.5

) to air (

n_2=1.0

Example 3

easy

Find the critical angle for light going from water (

n_1=1.33

) to air (

n_2=1.0

Example 4

easy

Light in glass hits the glass-air boundary at an angle greater than the critical angle. What happens?

Example 5

easy

Is the incidence angle in TIR measured from the surface or from the normal?

Example 6

easy

Can total internal reflection occur for light going from air into water?

Example 7

easy

A material has critical angle

\theta_c

to air given by

\sin\theta_c = 0.5

. Find

\theta_c

Example 8

easy

In an optical fiber, light stays inside by repeatedly undergoing what process?

Example 9

medium

A diamond has

n_1 = 2.42

. Find its critical angle in air.

Example 10

medium

Light in glass (

n=1.5

) hits the glass-air boundary at

45^\circ

. Does it undergo TIR? (Critical angle

\approx 41.8^\circ

Example 11

medium

Light in glass (

n=1.5

) hits the boundary to water (

n=1.33

). Find the critical angle.

Example 12

medium

A 45-45-90 prism is used to turn light by 90 degrees using TIR. The glass has

n=1.5

. The light hits the hypotenuse face at

45^\circ

. Does TIR occur there?

Example 13

medium

A material is submerged in water (

n=1.33

). The material-water critical angle is

50^\circ

. Find the material's index.

Example 14

medium

Light in glass (

n=1.5

) hits a glass-air boundary at

30^\circ

(below the

41.8^\circ

critical angle). What happens to the light?

Example 15

challenge

Light passes from medium A (

n=1.6

) into medium B, and the critical angle measured is

60^\circ

. Find

n_B

, then state whether TIR could occur going B to A.

Example 16

challenge

A fiber core has

n=1.50

and cladding

n=1.45

. Find the critical angle at the core-cladding boundary.

Example 17

challenge

Light in glass (

n=1.5

) just reaches the critical angle to air. What is the refraction angle of the light at that instant?

Example 18

medium

Light in water (

n=1.33

) hits the water-air surface at

50^\circ

. The critical angle is about

48.8^\circ

. Does TIR occur?

Example 19

medium

A glass-air critical angle is

42^\circ

. Light hits the boundary at exactly

42^\circ

. What is the refraction angle?

Example 20

medium

A liquid has refractive index

n=1.40

. Find its critical angle in air.

Example 21

easy

Write the formula for the critical angle

\theta_c

when light travels from medium 1 (

n_1

) into medium 2 (

n_2

) with

n_1 > n_2

Example 22

easy

Light goes from a medium with

n_1 = 2.0

to air (

n_2 = 1.0

). Find the critical angle.

Example 23

easy

Why can total internal reflection never occur when light goes from a less dense to a more dense medium?

Example 24

medium

Light in water (

n = 1.33

) strikes the water-air surface at

50^\circ

from the normal. Does it undergo TIR?

Example 25

medium

A substance has critical angle

42^\circ

in air. Find its refractive index.

Example 26

medium

Light in a medium with

n_1 = 1.6

meets a boundary to a medium with

n_2 = 1.4

65^\circ

. Does TIR occur?

Example 27

medium

A diver looks straight up from underwater. Light from the sky reaches the diver from a circular 'window'. What is the half-angle (in water) of that window? (

n_{\text{water}} = 1.33

)

Example 28

medium

A glass with

n = 1.5

is coated with a film of

n = 1.7

. For light inside the glass hitting the interface, can TIR occur there?

Example 29

medium

The critical angle for diamond (

n=2.42

) in air is about

24.4^\circ

. Compared to glass, why does diamond sparkle so strongly?

Example 30

hard

A swimmer underwater shines a laser upward. As she tilts the beam from vertical, at what tilt (relative to vertical) does the beam stop emerging into the air? (

n_{\text{water}} = 1.33

)

Example 31

hard

A glass slab (

n = 1.55

) is immersed in oil (

n = 1.45

). Find the critical angle for light going from glass into oil.

Example 32

hard

In one TIR bounce inside a fiber, the ray axis makes angle

\theta

with the surface. If

\theta = 4^\circ

, find the incidence angle from the normal and check TIR for a core/cladding boundary with

\theta_c = 80^\circ

Example 33

easy

A material has

\sin\theta_c = 0.8

in air. Find

n

Example 34

medium

In a Porro prism (used in binoculars), light hits each TIR face at

45^\circ

. What is the minimum glass index that guarantees TIR at the face when surrounded by air?

Example 35

easy

Why does a film of water on a windshield reduce the critical angle for light traveling from glass into the wet windshield surface?

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Related Concepts

Refraction Lenses

Background Knowledge

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

refraction