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Medium 1 (n₁ = 1.5)Medium 2 (n₂ = 1.0)Normalθ₁θ₂
Laser Ray

Live Telemetry & Summary

Observe Snell's Law bending. If $n_1 > n_2$, increase the incident angle past the critical angle to observe Total Internal Reflection (TIR).

Refraction Angle (θ₂):48.59°
Critical Angle (θ_c):41.81°
TIR Occurring:No

Variable Adjuster

Medium 1 Index (n₁)1.5
12
Medium 2 Index (n₂)1
12
Incident Angle (θ₁)30°
080

Refraction & Snell's Law

REFRA

Refraction is the bending of a wave when it enters a medium where its speed changes. Snell's Law relates the indices of refraction of the two media to the angles of incidence and refraction. Total Internal Reflection (TIR) occurs when light travels from a denser to rarer medium at an angle exceeding the critical angle.

n1sin⁡θ1=n2sin⁡θ2,θc=arcsin⁡(n2n1)n_1 \sin\theta_1 = n_2 \sin\theta_2, \quad \theta_c = \arcsin\left(\frac{n_2}{n_1}\right)

Whiteboard Solver Steps

Step 1

Snell's Law of Refraction

Light bends as it transitions between media of different refractive indices. If it enters a denser medium (higher n), it bends towards the normal line.

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2
Step 2

Critical Angle Condition

When traveling from a higher index medium to a lower index medium, the critical angle defines the incident threshold above which light cannot refract.

θc=arcsin⁡(n2n1)=arcsin⁡(11.5)≈41.81∘\theta_c = \arcsin\left(\frac{n_2}{n_1}\right) = \arcsin\left(\frac{1}{1.5}\right) \approx 41.81^\circ
Step 3

Refraction Angle Calculation

Light enters the second medium and refracts at an angle of approximately 48.59° relative to the boundary normal.

θ2=arcsin⁡(n1sin⁡θ1n2)=arcsin⁡(1.5sin⁡(30∘)1)≈48.59∘\theta_2 = \arcsin\left( \frac{n_1 \sin\theta_1}{n_2} \right) = \arcsin\left( \frac{1.5 \sin(30^\circ)}{1} \right) \approx 48.59^\circ