Refraction Examples in Physics

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

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 change in direction of a wave as it passes from one medium into another where it travels at a different speed.

A straw looks bent in a glass of water because light bends at the surface.

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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: Refraction asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to refraction but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?

Worked Examples

Example 1

medium
Light passes from air (n1=1.0n_1 = 1.0) into glass (n2=1.5n_2 = 1.5) at an angle of incidence of 30°30°. What is the angle of refraction?

Answer

θ2≈19.5°\theta_2 \approx 19.5°

First step

1
Apply Snell's law: n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2.

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Example 2

hard
What is the critical angle for light going from glass (n=1.5n = 1.5) to air (n=1.0n = 1.0)?

Example 3

medium
Light enters a glass slab (n=1.5n = 1.5) at 60°60° from the normal. Find the angle inside the glass and verify it leaves the parallel exit face at 60°60°.

Example 4

hard
Find the critical angle for light traveling from diamond (n=2.42n = 2.42) into air.

Example 5

medium
A fish 1.0 m1.0 \text{ m} below the water surface (n=1.33n = 1.33) is viewed from directly above. At what apparent depth does it appear?

Example 6

hard
A light ray hits the top of a glass cube (n=1.5n = 1.5) at 40°40° from the normal. What is the angle the refracted ray makes with the vertical (axis of the cube)?

Example 7

hard
White light contains red (nglass=1.51n_{glass} = 1.51) and violet (nglass=1.53n_{glass} = 1.53). Both enter a glass prism at 50°50° from the normal. Find the angle difference between the refracted rays inside the glass.

Example 8

challenge
A swimming pool 2 m2 \text{ m} deep is filled with water (n=1.33n=1.33). A small object on the bottom appears displaced when viewed at 40°40° from the vertical. Estimate the horizontal displacement of the apparent position from the actual position. (Use Snell's law approximation.)

Example 9

medium
A fiber optic cable has core n1=1.50n_1 = 1.50 and cladding n2=1.46n_2 = 1.46. Find the critical angle at the core-cladding boundary.

Example 10

hard
Light passes through a 4 cm4 \text{ cm} glass slab (n=1.5n=1.5) at incidence 30°30°. Find the lateral shift of the emerging beam.

Practice Problems

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

Example 1

medium
Light travels from water (n=1.33n = 1.33) into air (n=1.0n = 1.0) at an angle of incidence of 30°30°. What is the angle of refraction?

Example 2

hard
Light enters a diamond (n=2.42n = 2.42) from air (n=1.00n = 1.00) at an angle of incidence of 45°45°. Find the angle of refraction. Then calculate the critical angle for light leaving diamond into air.

Example 3

easy
State Snell's law relating the angles and indices at a boundary.

Example 4

easy
When light enters a denser medium (higher nn), does it bend toward or away from the normal?

Example 5

easy
When light refracts into a new medium, which stays the same: frequency or wavelength?

Example 6

easy
Light goes from air (n1=1n_1 = 1) into glass (n2=1.5n_2 = 1.5) at θ1=0∘\theta_1 = 0^\circ. Find θ2\theta_2.

Example 7

easy
The refractive index of a medium is n=1.5n = 1.5. By what factor is the speed of light slower than in vacuum?

Example 8

easy
Light in glass (n=1.5n = 1.5) has vacuum speed reference c=3×108c = 3\times10^8 m/s. Find its speed in the glass.

Example 9

easy
As light leaves glass and enters air (lower nn), does it bend toward or away from the normal?

Example 10

easy
Why does a straw in a glass of water appear bent?

Example 11

medium
Light goes from air (n1=1n_1 = 1) into water (n2=1.33n_2 = 1.33) at θ1=30∘\theta_1 = 30^\circ. Find sin⁡(θ2)\sin(\theta_2).

Example 12

medium
Light goes from glass (n1=1.5n_1 = 1.5) into air (n2=1n_2 = 1) at θ1=30∘\theta_1 = 30^\circ. Find sin⁡(θ2)\sin(\theta_2).

Example 13

medium
Light of wavelength 600600 nm in vacuum enters glass with n=1.5n = 1.5. Find its wavelength in the glass.

Example 14

medium
A medium has light speed v=1.5×108v = 1.5\times10^8 m/s. Find its refractive index (use c=3×108c = 3\times10^8 m/s).

Example 15

medium
Light enters a medium and bends toward the normal. Compared to vacuum, is the medium's index greater or less than 1, and does light speed up or slow down?

Example 16

medium
Light passes from medium A (n=1.2n = 1.2) to medium B at θ1=20∘\theta_1 = 20^\circ, and the refracted angle is also 20∘20^\circ. What is nBn_B?

Example 17

medium
A ray hits an air-glass boundary at θ1=60∘\theta_1 = 60^\circ (n1=1,n2=1.5n_1 = 1, n_2 = 1.5). Find sin⁡(θ2)\sin(\theta_2). (sin⁡60∘≈0.866\sin 60^\circ \approx 0.866)

Example 18

medium
Light slows from 3×1083\times10^8 m/s in vacuum to 2.4×1082.4\times10^8 m/s in a plastic. Find the plastic's refractive index.

Example 19

medium
A diamond has refractive index n=2.4n = 2.4. Find the speed of light inside it (use c=3×108c = 3\times10^8 m/s).

Example 20

challenge
Find the critical angle for total internal reflection at a glass-air boundary, nglass=1.5n_{glass} = 1.5, nair=1n_{air} = 1.

Example 21

challenge
Light passes from water (n=1.33n = 1.33) through a flat boundary into glass (n=1.5n = 1.5) at θ1=40∘\theta_1 = 40^\circ. Find sin⁡(θ2)\sin(\theta_2). (sin⁡40∘≈0.643\sin 40^\circ \approx 0.643)

Example 22

challenge
A ray enters a glass slab (n=1.5n = 1.5) from air at θ1=45∘\theta_1 = 45^\circ, then exits the parallel far side back into air. What is the exit angle relative to the original direction?

Example 23

easy
Light passes from air (n=1.00n = 1.00) into water (n=1.33n = 1.33) at 45°45° from the normal. Find the angle of refraction.

Example 24

easy
The speed of light in a medium is 2.0×108 m/s2.0 \times 10^8 \text{ m/s}. What is the medium's refractive index?

Example 25

medium
Light of wavelength 600 nm600 \text{ nm} in vacuum enters water (n=1.33n = 1.33). What is the wavelength inside the water?

Example 26

medium
Light hits a glass-air interface from the glass side (n=1.5n = 1.5) at 30°30°. Find the angle of refraction in air.

Example 27

easy
Sound travels faster in warm air. A sound wave going from cool air into warm air bends ___ the normal.

Example 28

medium
Light goes from medium A (n=1.2n = 1.2) to medium B (n=1.6n = 1.6) at 50°50° to normal. Find the refraction angle.

Example 29

medium
Find the critical angle for light going from water (n=1.33n = 1.33) into air.

Example 30

easy
A ray normally incident on a flat glass surface refracts at what angle?

Example 31

medium
Light enters glass (n=1.5n=1.5) from air at 0°0° to the surface (grazing). What is the angle of refraction?

Example 32

medium
Light incident at 25°25° to normal refracts at 18°18° in a medium. Find the medium's refractive index (light from air).

Example 33

medium
Light in water (n=1.33n=1.33) has speed of how much?

Example 34

easy
When light enters a medium with n=2.0n = 2.0, its speed becomes ___ of the speed in vacuum.

Example 35

medium
A ray traveling in glass (n=1.5n=1.5) hits the glass-air interface at 50°50°. Does it refract or totally internally reflect?
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Background Knowledge

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

waveswave speed