Refraction Formula

The Formula

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

n_1 and n_2 are the refractive indices (dimensionless), \theta_1 is the angle of incidence, \theta_2 is the angle of refraction, c is the speed of light in vacuum, and v 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 n_1 \sin\theta_1 = n_2 \sin\theta_2, where the refractive index n = c/v is the ratio of the speed of light in vacuum to the speed in the medium. When n_1 \sin\theta_1 > n_2, total internal reflection occurs.

Worked Examples

Example 1

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

Solution

  1. 1
    Apply Snell's law: n_1 \sin\theta_1 = n_2 \sin\theta_2.
  2. 2
    1.0 \times \sin 30° = 1.5 \times \sin\theta_2
  3. 3
    0.5 = 1.5 \sin\theta_2 \implies \sin\theta_2 = \frac{0.5}{1.5} = 0.333
  4. 4
    \theta_2 = \sin^{-1}(0.333) \approx 19.5°

Answer

\theta_2 \approx 19.5°
Refraction occurs when light changes speed as it enters a different medium. Light bends toward the normal when entering a denser medium (higher refractive index).

Example 2

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

Common Mistakes

  • Confusing the direction of bending — light bends toward the normal when entering a denser medium (higher n), not away from it.
  • 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.
  • Applying Snell's law with angles measured from the surface instead of from the normal — all angles must be measured from the perpendicular.

Why This Formula Matters

Refraction is the principle behind lenses in eyeglasses, cameras, microscopes, and telescopes. It explains why swimming pools appear shallower than they are, why prisms split white light into a rainbow, and how fibre-optic cables guide light over long distances.

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?

n_1 and n_2 are the refractive indices (dimensionless), \theta_1 is the angle of incidence, \theta_2 is the angle of refraction, c is the speed of light in vacuum, and v is the speed of light in the medium.

Why is the Refraction formula important in Physics?

Refraction is the principle behind lenses in eyeglasses, cameras, microscopes, and telescopes. It explains why swimming pools appear shallower than they are, why prisms split white light into a rainbow, and how fibre-optic cables guide light over long distances.

What do students get wrong about Refraction?

Light bends toward the normal when entering a slower medium.

What should I learn before the Refraction formula?

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

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