Snells Law Worksheet | PDF | Refraction | Refractive Index - Free Printable

Let’s solve each problem step by step.

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Problem 1:
A ray of light traveling from air into crown glass strikes the surface at an angle of 30 degrees. What will be the angle of refraction?

We use Snell’s Law:
> n₁ × sin(θ₁) = n₂ × sin(θ₂)

Where:
- n₁ = index of refraction of first medium (air) → from table: 1.00
- θ₁ = angle of incidence → 30°
- n₂ = index of refraction of second medium (crown glass) → from table: 1.52
- θ₂ = angle of refraction → what we’re solving for

Plug in the numbers:

1.00 × sin(30°) = 1.52 × sin(θ₂)

sin(30°) = 0.5

So:

0.5 = 1.52 × sin(θ₂)

Now divide both sides by 1.52:

sin(θ₂) = 0.5 / 1.52 ≈ 0.3289

Now take inverse sine (arcsin):

θ₂ = arcsin(0.3289) ≈ 19.2°

✔ So, the angle of refraction is about 19.2 degrees.

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Problem 2:
Light traveling through air encounters a second medium which slows the light to 2.7 × 10⁸ m/s. What is the index of the second medium?

The speed of light in vacuum (or approximately in air) is c = 3.0 × 10⁸ m/s.

Index of refraction n = c / v

Where:
- c = 3.0 × 10⁸ m/s
- v = 2.7 × 10⁸ m/s

n = (3.0 × 10⁸) / (2.7 × 10⁸) = 3.0 / 2.7 ≈ 1.11

✔ So, the index of refraction of the second medium is 1.11

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Problem 3:
Light travels through a substance at 1.97 × 10⁸ m/s. What is the index of the liquid? What type of liquid is it?

Again, use n = c / v

c = 3.0 × 10⁸ m/s
v = 1.97 × 10⁸ m/s

n = 3.0 / 1.97 ≈ 1.52

Looking at the table provided:

- Crown Glass: 1.52 ← matches!

But wait — the question says “liquid”. Crown glass is solid. Let’s check the table again:

Table shows:
- Air or vacuum: 1.00
- Water: 1.33
- CR39 Plastic: 1.498
- Crown Glass: 1.52
- Barium glass: 1.60
- Flint glass: 1.70
- Polycarbonate: 1.586
- Diamond: 2.45

None of these are liquids except water (1.33). But 1.52 doesn’t match any liquid listed.

Wait — maybe there’s a mistake? Or perhaps the question expects us to say “Crown Glass” even though it’s not a liquid? That doesn’t make sense.

Alternatively — maybe the value 1.52 corresponds to some other liquid not listed, but based on the table given, nothing matches.

Hold on — let me double-check calculation:

3.0 ÷ 1.97 = ?

Do exact division:

3.0000 ÷ 1.97 = ?

1.97 × 1.52 = 1.97 × 1.5 = 2.955; 1.97 × 0.02 = 0.0394 → total 2.9944 → close to 3.0

Yes, so n ≈ 1.523 → rounds to 1.52

In real life, some oils or organic liquids can have refractive indices around 1.5, but according to the table provided, no liquid has n=1.52.

However — looking back at the table, “CR39 Plastic” is 1.498 ≈ 1.50, and “Polycarbonate” is 1.586 — neither is 1.52.

Wait — perhaps the question meant to say “substance”, not necessarily liquid? But it specifically says “liquid”.

Maybe it’s a trick? Or typo?

Actually — let’s look again: the table includes “Water: 1.33”, and that’s the only liquid. So if the answer must come from the table, then none match.

But perhaps in context of this worksheet, they expect you to pick the closest material — which is Crown Glass (1.52) — even though it’s not a liquid.

Alternatively — maybe the student is supposed to realize that no liquid in the table matches, so perhaps write “not listed” or something.

But since this is likely a standard homework problem, and many textbooks list “carbon disulfide” or “benzene” as having n≈1.5–1.6, but those aren’t in the table.

Given the constraints of the table provided, and since 1.52 exactly matches Crown Glass, I think the intended answer is:

→ Index = 1.52
→ Type = Crown Glass (even though it’s not a liquid — possibly an error in question wording)

OR — perhaps the question meant “material” instead of “liquid”.

To stay faithful to the table and math:

✔ Final Answer for Problem 3:
Index = 1.52
Material = Crown Glass (based on table match)

If strict about “liquid”, then no match — but since the table doesn’t include other liquids, we go with best fit.

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Final Answers:

Problem 1: 19.2°
Problem 2: 1.11
Problem 3: Index = 1.52, Material = Crown Glass

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Final Answer:
1. 19.2°
2. 1.11
3. Index: 1.52, Material: Crown Glass