MotionLab

Snell's Law Calculator

Why a straw looks bent in a glass of water — light bending as it crosses between materials.

Refractive index 1 (n₁)

Angle of incidence (°)

Refractive index 2 (n₂)

Angle of refraction (°)

22.082

n₁sin(θ₁) = n₂sin(θ₂)

What you entered

Refractive index 1 (n₁): 1Angle of incidence (°): 30Refractive index 2 (n₂): 1.33

1
θ₂ = asin(n₁sin(θ₁) ÷ n₂)
asin(1×sin(30°) ÷ 1.33)= 22.0824°

Result

Angle of refraction (°): 22.082

Light entering at 30° from a medium with n₁=1 into n₂=1.33 refracts to 22.08°.

Refraction angles at common interfaces

Snell's law: n1 sin theta1 equals n2 sin theta2. Light bends toward the normal when entering a denser medium.

n1	Angle in (deg)	n2	Angle out (deg)	Interface
1	30	1.33	22.082	Air into water
1	30	1.5	19.471	Air into glass
1	45	1.5	28.126	Air into glass, steeper
1	60	2.42	20.969	Air into diamond
1.33	30	1	41.682	Water into air

The last row runs the other way and the ray bends away from the normal, which is why a submerged object appears shallower than it is and why a straw looks bent at the waterline. Push that angle further and beyond the critical angle - about 48.8 degrees for water to air - the light stops escaping entirely and reflects internally, which is the principle behind fibre optics. Diamond's very high index of 2.42 gives it a critical angle near 24 degrees, trapping light inside and producing the characteristic sparkle.

Why light bends at all

Light travels at different speeds in different materials (slower in denser optical media like water or glass) — this speed change causes the wave to bend, similar to how a wheel pulls to one side if one wheel hits mud while the other stays on pavement.

Total internal reflection

When light travels from a denser to a less dense medium at a steep enough angle, Snell's law has no valid solution — light can't refract out at all and instead reflects entirely back into the denser medium, which is how fiber optic cables work.

Frequently asked questions

Light enters water (n = 1.33) from air (n = 1.0) at 45°. What's the refraction angle?

sin(θ₂) = n₁sin(θ₁)/n₂ = 1.0 × sin(45°)/1.33 = 0.707/1.33 = 0.532. θ₂ = 32.1°. The light bends toward the normal (closer to perpendicular) because water is optically denser.

What is the critical angle for total internal reflection in glass?

For glass (n = 1.5) to air (n = 1.0): sin(θ_c) = n₂/n₁ = 1/1.5 = 0.667. θ_c = 41.8°. Any light hitting the glass-air boundary at more than 41.8° from the normal reflects entirely — this is how fiber optics trap light inside the fiber.

Why do swimming pools look shallower than they are?

Light bending at the water-air interface makes submerged objects appear closer to the surface. The apparent depth is actual depth × (n_air/n_water) = depth × (1/1.33) ≈ 75% of actual depth. A 2 m pool looks about 1.5 m deep.