Total Internal Reflection Examples in Physics

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 (n1=1.50n_1 = 1.50) is surrounded by cladding (n2=1.45n_2 = 1.45). Find the critical angle at the core-cladding boundary.

Answer

θc≈75.2∘\theta_c \approx 75.2^\circ

First step

1
sin⁡θc=1.45/1.50=0.9667\sin\theta_c = 1.45/1.50 = 0.9667.

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Example 2

medium
A right-angle prism (n=1.52n=1.52) is used as a periscope element. Light enters the long face normally and hits the hypotenuse at 45∘45^\circ. Does it TIR off the hypotenuse?

Example 3

medium
Light travels from glass (n=1.52n=1.52) into water (n=1.33n=1.33). Find the critical angle.

Example 4

medium
Light is incident on a glass-air boundary (nglass=1.50n_{\text{glass}}=1.50) at 35∘35^\circ. Find the refracted angle in air.

Example 5

hard
A fiber has core index n1=1.50n_1 = 1.50 and cladding n2=1.46n_2 = 1.46. Find the maximum acceptance angle θa\theta_a in air for a ray that will be guided by TIR.

Example 6

hard
A cubic glass block (n=1.50n=1.50) sits in air. A horizontal laser enters one vertical face at 20∘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 n1=1.65n_1 = 1.65 into another with n2=1.33n_2 = 1.33.

Example 8

medium
Show that the critical angle for crown glass (n=1.52n=1.52) in air is about 41.1∘41.1^\circ.

Example 9

medium
Find the critical angle for light passing from a glass with n1=1.75n_1 = 1.75 into air.

Example 10

challenge
A point source sits 1.0 m1.0\,\text{m} below the surface of a calm lake (n=1.33n=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 n1=1.48n_1 = 1.48 and cladding n2=1.46n_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 (n1=1.5n_1=1.5) to air (n2=1.0n_2=1.0).

Example 3

easy
Find the critical angle for light going from water (n1=1.33n_1=1.33) to air (n2=1.0n_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 θc\theta_c to air given by sin⁡θc=0.5\sin\theta_c = 0.5. Find θc\theta_c.

Example 8

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

Example 9

medium
A diamond has n1=2.42n_1 = 2.42. Find its critical angle in air.

Example 10

medium
Light in glass (n=1.5n=1.5) hits the glass-air boundary at 45∘45^\circ. Does it undergo TIR? (Critical angle ≈41.8∘\approx 41.8^\circ.)

Example 11

medium
Light in glass (n=1.5n=1.5) hits the boundary to water (n=1.33n=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=1.5n=1.5. The light hits the hypotenuse face at 45∘45^\circ. Does TIR occur there?

Example 13

medium
A material is submerged in water (n=1.33n=1.33). The material-water critical angle is 50∘50^\circ. Find the material's index.

Example 14

medium
Light in glass (n=1.5n=1.5) hits a glass-air boundary at 30∘30^\circ (below the 41.8∘41.8^\circ critical angle). What happens to the light?

Example 15

challenge
Light passes from medium A (n=1.6n=1.6) into medium B, and the critical angle measured is 60∘60^\circ. Find nBn_B, then state whether TIR could occur going B to A.

Example 16

challenge
A fiber core has n=1.50n=1.50 and cladding n=1.45n=1.45. Find the critical angle at the core-cladding boundary.

Example 17

challenge
Light in glass (n=1.5n=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=1.33n=1.33) hits the water-air surface at 50∘50^\circ. The critical angle is about 48.8∘48.8^\circ. Does TIR occur?

Example 19

medium
A glass-air critical angle is 42∘42^\circ. Light hits the boundary at exactly 42∘42^\circ. What is the refraction angle?

Example 20

medium
A liquid has refractive index n=1.40n=1.40. Find its critical angle in air.

Example 21

easy
Write the formula for the critical angle θc\theta_c when light travels from medium 1 (n1n_1) into medium 2 (n2n_2) with n1>n2n_1 > n_2.

Example 22

easy
Light goes from a medium with n1=2.0n_1 = 2.0 to air (n2=1.0n_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=1.33n = 1.33) strikes the water-air surface at 50∘50^\circ from the normal. Does it undergo TIR?

Example 25

medium
A substance has critical angle 42∘42^\circ in air. Find its refractive index.

Example 26

medium
Light in a medium with n1=1.6n_1 = 1.6 meets a boundary to a medium with n2=1.4n_2 = 1.4 at 65∘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? (nwater=1.33n_{\text{water}} = 1.33)

Example 28

medium
A glass with n=1.5n = 1.5 is coated with a film of n=1.7n = 1.7. For light inside the glass hitting the interface, can TIR occur there?

Example 29

medium
The critical angle for diamond (n=2.42n=2.42) in air is about 24.4∘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? (nwater=1.33n_{\text{water}} = 1.33)

Example 31

hard
A glass slab (n=1.55n = 1.55) is immersed in oil (n=1.45n = 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 θ\theta with the surface. If θ=4∘\theta = 4^\circ, find the incidence angle from the normal and check TIR for a core/cladding boundary with θc=80∘\theta_c = 80^\circ.

Example 33

easy
A material has sin⁡θc=0.8\sin\theta_c = 0.8 in air. Find nn.

Example 34

medium
In a Porro prism (used in binoculars), light hits each TIR face at 45∘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

RefractionLenses

Background Knowledge

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

refraction