Refraction Worksheet - ololl - Index of Refraction & Snells ... - Free Printable

Let’s solve each problem step by step. We’ll use the key formula:

Index of refraction (n) = speed of light in vacuum (c) / speed of light in medium (v)
→ So, v = c / n and n = c / v

We know:
c = 3.00 × 10⁸ m/s (speed of light in vacuum — we always use this unless told otherwise)

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Problem 1: Calculate speed of light in mediums

Use: v = c / n

a. Water (n=1.33):
v = 3.00e8 / 1.33 ≈ 2.26 × 10⁸ m/s

b. Diamond (n=2.42):
v = 3.00e8 / 2.42 ≈ 1.24 × 10⁸ m/s

c. Plexiglas (n=1.51):
v = 3.00e8 / 1.51 ≈ 1.99 × 10⁸ m/s

✔ Checked calculations — all correct.

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Problem 2: Find refractive index if speed is given

Use: n = c / v

a. v = 2.10 × 10⁸ m/s
n = 3.00e8 / 2.10e8 = 1.43

b. v = 1.50 × 10⁸ m/s
n = 3.00e8 / 1.50e8 = 2.00

✔ Simple division — no errors.

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Problem 3: Speed in your own material (n=1.10)

v = c / n = 3.00e8 / 1.10 ≈ 2.73 × 10⁸ m/s

✔ Correct.

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Problem 4: Angle of refraction from air to medium at incidence angle 25.0°

Use Snell’s Law:
n₁ sinθ₁ = n₂ sinθ₂

Air has n₁ ≈ 1.00
θ₁ = 25.0°
So: sinθ₂ = (n₁ / n₂) × sinθ₁ = (1.00 / n₂) × sin(25.0°)

First, calculate sin(25.0°) ≈ 0.4226

a. Water (n=1.33):
sinθ₂ = (1/1.33) × 0.4226 ≈ 0.3177 → θ₂ = arcsin(0.3177) ≈ 18.5°

b. Diamond (n=2.42):
sinθ₂ = (1/2.42) × 0.4226 ≈ 0.1746 → θ₂ = arcsin(0.1746) ≈ 10.1°

c. Plexiglas (n=1.51):
sinθ₂ = (1/1.51) × 0.4226 ≈ 0.2799 → θ₂ = arcsin(0.2799) ≈ 16.3°

✔ All angles calculated correctly using calculator.

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Problem 5: Incidence 20.0° in water → refraction 15°

Water n₁ = 1.33, θ₁ = 20.0°, θ₂ = 15°

a. Is second medium more or less optically dense?

Since light bends toward the normal (angle got smaller: 20° → 15°), it entered a more optically dense medium.

✔ Logic check: bending toward normal = higher n.

b. Find n of second medium

Snell’s Law: n₁ sinθ₁ = n₂ sinθ₂
→ n₂ = (n₁ sinθ₁) / sinθ₂
= (1.33 × sin20.0°) / sin15°
sin20° ≈ 0.3420, sin15° ≈ 0.2588
n₂ = (1.33 × 0.3420) / 0.2588 ≈ 0.4549 / 0.2588 ≈ 1.76

✔ Calculation verified.

c. Speed of light in each medium

In water: v₁ = c / n₁ = 3.00e8 / 1.33 ≈ 2.26 × 10⁸ m/s

In second medium: v₂ = c / n₂ = 3.00e8 / 1.76 ≈ 1.70 × 10⁸ m/s

✔ Correct.

d. Repeat for refraction angle 25.0°

Now θ₂ = 25.0°, θ₁ = 20.0°, n₁ = 1.33

Find n₂:
n₂ = (n₁ sinθ₁) / sinθ₂ = (1.33 × sin20°) / sin25°
= (1.33 × 0.3420) / 0.4226 ≈ 0.4549 / 0.4226 ≈ 1.08

Is it more or less dense? Since angle increased (20° → 25°), light bent away from normal → less optically dense.

Speeds:

v₁ (water) = same as before: 2.26 × 10⁸ m/s

v₂ = c / n₂ = 3.00e8 / 1.08 ≈ 2.78 × 10⁸ m/s

✔ All steps checked.

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Problem 6: Light travels 875 km in 5.00 ms in material “x”

First, convert units:

Distance = 875 km = 875,000 m = 8.75 × 10⁵ m

Time = 5.00 ms = 0.005 s = 5.00 × 10⁻³ s

Speed v = distance / time = 8.75e5 / 5.00e-3 = 1.75 × 10⁸ m/s

Now find index of refraction:

n = c / v = 3.00e8 / 1.75e8 ≈ 1.71

✔ Units converted correctly, math verified.

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Final Answer:

1.
a. 2.26 × 10⁸ m/s
b. 1.24 × 10⁸ m/s
c. 1.99 × 10⁸ m/s

2.
a. 1.43
b. 2.00

3. 2.73 × 10⁸ m/s

4.
a. 18.5°
b. 10.1°
c. 16.3°

5.
a. More optically dense
b. 1.76
c. Water: 2.26 × 10⁸ m/s; Second medium: 1.70 × 10⁸ m/s
d. n = 1.08; Less optically dense; Speeds: water 2.26 × 10⁸ m/s, second medium 2.78 × 10⁸ m/s

6. Speed = 1.75 × 10⁸ m/s; Index of refraction = 1.71