Refraction Formula

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

The Formula

n1sin⁡(θ1)=n2sin⁡(θ2)n_1 \sin(\theta_1) = n_2 \sin(\theta_2) (Snell's Law)

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

Quick Example

Lenses focus light by refraction; a pool looks shallower than it is.

Notation

n1n_1 and n2n_2 are the refractive indices (dimensionless), θ1\theta_1 is the angle of incidence, θ2\theta_2 is the angle of refraction, cc is the speed of light in vacuum, and vv is the speed of light in the medium.

What This Formula Means

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.

Formal View

Snell's law of refraction is n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2, where the refractive index n=c/vn = c/v is the ratio of the speed of light in vacuum to the speed in the medium. When n1sin⁡θ1>n2n_1 \sin\theta_1 > n_2, total internal reflection occurs.

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°.

Common Mistakes

  • Confusing the direction of bending — light bends toward the normal when entering a denser medium (higher nn), not away from it. - Fix this by naming the system, checking "Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?", and attaching units or direction to the final statement.
  • Forgetting that the wave speed changes but the frequency stays the same — it is the wavelength that changes when a wave enters a new medium. - Fix this by naming the system, checking "Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?", and attaching units or direction to the final statement.
  • Applying Snell's law with angles measured from the surface instead of from the normal — all angles must be measured from the perpendicular. - Fix this by naming the system, checking "Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?", and attaching units or direction to the final statement.
  • Using refraction from a keyword alone - Signal words like wave, frequency, wavelength only point to a possible model; the system must match too.

Why This Formula Matters

Refraction helps students connect sound, light, water waves, strings, and communication signals. The same wave habits explain music, optics, earthquakes, radio, and interference patterns.

Frequently Asked Questions

What is the Refraction formula?

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

How do you use the Refraction formula?

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

What do the symbols mean in the Refraction formula?

n1n_1 and n2n_2 are the refractive indices (dimensionless), θ1\theta_1 is the angle of incidence, θ2\theta_2 is the angle of refraction, cc is the speed of light in vacuum, and vv is the speed of light in the medium.

Why is the Refraction formula important in Physics?

Refraction helps students connect sound, light, water waves, strings, and communication signals. The same wave habits explain music, optics, earthquakes, radio, and interference patterns.

What do students get wrong about Refraction?

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.

What should I learn before the Refraction formula?

Before studying the Refraction formula, you should understand: waves, wave speed.

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