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Snell's Law worksheet

Grades 11–12 · CCSS HSF.TF.B.7

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Index n₂
- First medium (light comes from here): Vacuum: n = 1 (exact)
- Angle of incidence (θ₁): 42 °
- Angle of refraction (θ₂): 25 °
Find: Refractive index n₂
Answer
2.
Problem 2.
- Solve for: Incidence angle (θ₁)
- First medium (light comes from here): Water: n ≈ 1.333
- Second medium (light enters this): Vacuum: n = 1 (exact)
- Angle of refraction (θ₂): 17 °
Find: Incidence angle (θ₁)
Answer
3.
Problem 3.
- Solve for: Refraction angle (θ₂)
- First medium (light comes from here): Air: n ≈ 1.000293
- Second medium (light enters this): Glass: n ≈ 1.5
- Angle of incidence (θ₁): 20 °
Find: Refraction angle (θ₂)
Answer
4.
Problem 4.
- Solve for: Index n₂
- First medium (light comes from here): Glass: n ≈ 1.5
- Angle of incidence (θ₁): 26 °
- Angle of refraction (θ₂): 24 °
Find: Refractive index n₂
Answer
5.
Problem 5.
- Solve for: Index n₁
- Second medium (light enters this): Enter a refractive index
- Refractive index n₂: 1.2
- Angle of incidence (θ₁): 24 °
- Angle of refraction (θ₂): 18.25 °
Find: Refractive index n₁
Answer
6.
Problem 6.
- Solve for: Index n₂
- First medium (light comes from here): Enter a refractive index
- Refractive index n₁: 1.8
- Angle of incidence (θ₁): 36 °
- Angle of refraction (θ₂): 30 °
Find: Refractive index n₂
Answer
7.
Problem 7.
- Solve for: Refraction angle (θ₂)
- First medium (light comes from here): Vacuum: n = 1 (exact)
- Second medium (light enters this): Enter a refractive index
- Refractive index n₂: 1.4
- Angle of incidence (θ₁): 30 °
Find: Refraction angle (θ₂)
Answer
8.
Problem 8.
- Solve for: Refraction angle (θ₂)
- First medium (light comes from here): Enter a refractive index
- Refractive index n₁: 1.2
- Second medium (light enters this): Vacuum: n = 1 (exact)
- Angle of incidence (θ₁): 32 °
Find: Refraction angle (θ₂)
Answer
9.
Problem 9.
- Solve for: Index n₁
- Second medium (light enters this): Enter a refractive index
- Refractive index n₂: 1
- Angle of incidence (θ₁): 26 °
- Angle of refraction (θ₂): 15.25 °
Find: Refractive index n₁
Answer
10.
Problem 10.
- Solve for: Incidence angle (θ₁)
- First medium (light comes from here): Glass: n ≈ 1.5
- Second medium (light enters this): Glass: n ≈ 1.5
- Angle of refraction (θ₂): 19.5 °
Find: Incidence angle (θ₁)
Answer

Answer key: Snell's Law worksheet

1. Refractive index n₂: 1.58
1. Use the exact refractive index for vacuum
  $n₁$ $= 1$
2. Rearrange Snell's law to find the second material's index: n₂ = n₁ × sin θ₁ ÷ sin θ₂
  $\frac{1 \times 0.66913061}{0.42261826}$ $= 1.5832979$
2. Incidence angle (θ₁): 12.67 °
1. Use an approximate refractive index for water
  $n₁$ $= 1.333$
2. Use the exact refractive index for vacuum
  $n₂$ $= 1$
3. Rearrange Snell's law to find the sine of the incoming (incidence) angle: sin θ₁ = n₂ × sin θ₂ ÷ n₁
  $\frac{1 \times sin 17°}{1.333}$ $= \frac{1 \times 0.2923717}{1.333}$ $= 0.21933361$
4. Turn the sine back into an angle with the inverse sine (arcsin)
  $θ₁ = arcsin 0.21933361$ $= 12.669896 °$
5. Light is passing into a lower index, so there's a critical angle, past which all light reflects: θc = arcsin(n₂ ÷ n₁)
  $θc = arcsin \frac{1}{1.333}$ $= 48.606626 °$
3. Refraction angle (θ₂): 13.18 °
1. Use an approximate refractive index for air
  $n₁$ $= 1.000293$
2. Use an approximate refractive index for glass
  $n₂$ $= 1.5$
3. Rearrange Snell's law to find the sine of the bent (refraction) angle: sin θ₂ = n₁ × sin θ₁ ÷ n₂
  $\frac{1.000293 \times sin 20°}{1.5}$ $= \frac{1.000293 \times 0.34202014}{1.5}$ $= 0.22808024$
4. Turn the sine back into an angle with the inverse sine (arcsin)
  $θ₂ = arcsin 0.22808024$ $= 13.184074 °$
4. Refractive index n₂: 1.62
1. Use an approximate refractive index for glass
  $n₁$ $= 1.5$
2. Rearrange Snell's law to find the second material's index: n₂ = n₁ × sin θ₁ ÷ sin θ₂
  $\frac{1.5 \times 0.43837115}{0.40673664}$ $= 1.61666457$
5. Refractive index n₁: 0.92
1. Rearrange Snell's law to find the first material's index: n₁ = n₂ × sin θ₂ ÷ sin θ₁
  $\frac{1.2 \times 0.31316381}{0.40673664}$ $= 0.92393094$
6. Refractive index n₂: 2.12
1. Rearrange Snell's law to find the second material's index: n₂ = n₁ × sin θ₁ ÷ sin θ₂
  $\frac{1.8 \times 0.58778525}{0.5}$ $= 2.11602691$
7. Refraction angle (θ₂): 20.92 °
1. Use the exact refractive index for vacuum
  $n₁$ $= 1$
2. Rearrange Snell's law to find the sine of the bent (refraction) angle: sin θ₂ = n₁ × sin θ₁ ÷ n₂
  $\frac{1 \times sin 30°}{1.4}$ $= \frac{1 \times 0.5}{1.4}$ $= 0.35714286$
3. Turn the sine back into an angle with the inverse sine (arcsin)
  $θ₂ = arcsin 0.35714286$ $= 20.924832 °$
8. Refraction angle (θ₂): 39.49 °
1. Use the exact refractive index for vacuum
  $n₂$ $= 1$
2. Rearrange Snell's law to find the sine of the bent (refraction) angle: sin θ₂ = n₁ × sin θ₁ ÷ n₂
  $\frac{1.2 \times sin 32°}{1}$ $= \frac{1.2 \times 0.52991926}{1}$ $= 0.63590312$
3. Turn the sine back into an angle with the inverse sine (arcsin)
  $θ₂ = arcsin 0.63590312$ $= 39.486999 °$
4. Light is passing into a lower index, so there's a critical angle, past which all light reflects: θc = arcsin(n₂ ÷ n₁)
  $θc = arcsin \frac{1}{1.2}$ $= 56.44269 °$
9. Refractive index n₁: 0.6
1. Rearrange Snell's law to find the first material's index: n₁ = n₂ × sin θ₂ ÷ sin θ₁
  $\frac{1 \times 0.26303121}{0.43837115}$ $= 0.60001945$
10. Incidence angle (θ₁): 19.5 °
1. Use an approximate refractive index for glass
  $n₁$ $= 1.5$
2. Use an approximate refractive index for glass
  $n₂$ $= 1.5$
3. Rearrange Snell's law to find the sine of the incoming (incidence) angle: sin θ₁ = n₂ × sin θ₂ ÷ n₁
  $\frac{1.5 \times sin 19.5°}{1.5}$ $= \frac{1.5 \times 0.33380686}{1.5}$ $= 0.33380686$
4. Turn the sine back into an angle with the inverse sine (arcsin)
  $θ₁ = arcsin 0.33380686$ $= 19.5 °$