The Memory Trick
💡 n₁sin θ₁ = n₂sin θ₂
Snell's Law describes how light bends (refracts) when crossing the boundary between two materials with different refractive indices (n): n₁sin θ₁ = n₂sin θ₂, where θ₁ and θ₂ are the angles of incidence and refraction, both measured from the normal. A higher refractive index means light travels more slowly in that material, and correspondingly bends more sharply.
Why It Works
Light bends because its speed changes at the boundary between materials — going from a faster medium (lower n) to a slower medium (higher n), light bends TOWARD the normal; going from slower to faster, it bends AWAY from the normal. This directional rule is a direct, memorable consequence of Snell's Law.
Step by Step
Applying Snell's Law
1
Air to glass — bending toward the normal
Since glass has a higher refractive index than air, light slows down entering glass and bends TOWARD the normal line.
A pencil dipped into a glass of water appears to bend at the surface, exactly because light bends toward the normal as it enters the denser water.
2
Glass to air — bending away from the normal
Going the opposite direction (from a higher-n material back into a lower-n material like air), light speeds back up and bends AWAY from the normal.
Light exiting a glass prism back into air bends away from the normal, in the opposite direction from how it bent entering the prism.
3
Solving for an unknown angle or index
Given any three of the four quantities (n₁, θ₁, n₂, θ₂), Snell's Law lets you solve directly for the fourth.
Knowing the incidence angle in air and the refraction angle inside a material lets you calculate that material's unknown refractive index.
🏥 Worked Example
Light traveling in air (n=1.00) strikes a glass surface (n=1.5) at an angle of incidence of 40°. What is the angle of refraction inside the glass?
1
Apply Snell's Law: n₁sin θ₁ = n₂sin θ₂ → (1.00)sin(40°) = (1.5)sin θ₂.
2
Solve for sin θ₂: sin θ₂ = sin(40°)/1.5 ≈ 0.643/1.5 ≈ 0.4287.
3
Find θ₂: θ₂ = sin⁻¹(0.4287) ≈ 25.4° — smaller than the original 40°, confirming the light bent TOWARD the normal entering the denser glass, as expected.
📌 Exam Application
Exams test correctly applying Snell's Law to solve for an unknown angle or refractive index, and correctly reasoning about the DIRECTION of bending (toward or away from the normal) based on the relative refractive indices involved.
⚠️ Most Common Refraction — Snell's Law Mistakes
The most common trap is getting the bending direction backward — remember that light bends TOWARD the normal when entering a material with a HIGHER refractive index (slower light), and AWAY from the normal when entering a material with a LOWER refractive index (faster light).
✓ Quick Self-Test
1) Write Snell's Law. n₁sin θ₁ = n₂sin θ₂. 2) When light travels from air into glass, does it bend toward or away from the normal? Toward the normal. 3) When light travels from glass back into air, does it bend toward or away from the normal? Away from the normal. 4) What does a higher refractive index indicate about how fast light travels in that material? Light travels more slowly in a material with a higher refractive index. 5) Why does a pencil appear bent when partially submerged in a glass of water? Light reflecting off the submerged portion refracts (bends toward the normal) upon exiting the water into air, creating an apparent discontinuity at the surface.