Question

A ray of light passes from air into water at an incident angle of 60°. Which of the following is the angle of refraction? Note: nwater=1.36.

Group of answer choices

90.0°

36.5°

66.0°

39.5°

Answer 1

To find the angle of refraction when light passes from air into water, we can use Snell's Law, which is given by the formula:

\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\]

where:
- \( n_1 \) is the index of refraction of the first medium (air, approximately 1.00),
- \( \theta_1 \) is the angle of incidence,
- \( n_2 \) is the index of refraction of the second medium (water, given as 1.36),
- \( \theta_2 \) is the angle of refraction.

Given:
- \( n_1 = 1.00 \)
- \( \theta_1 = 60° \)
- \( n_2 = 1.36 \)

We can rearrange Snell's Law to solve for \( \theta_2 \):

\[
\sin(\theta_2) = \frac{n_1 \sin(\theta_1)}{n_2}
\]

Now substituting the values:

\[
\sin(\theta_2) = \frac{1.00 \times \sin(60°)}{1.36}
\]

Calculating \( \sin(60°) \):

\[
\sin(60°) = \frac{\sqrt{3}}{2} \approx 0.866
\]

Now substituting this value into the formula:

\[
\sin(\theta_2) = \frac{1.00 \times 0.866}{1.36} \approx \frac{0.866}{1.36} \approx 0.6368
\]

Now we find \( \theta_2 \) by taking the inverse sine:

\[
\theta_2 = \sin^{-1}(0.6368)
\]

Calculating \( \theta_2 \):

\[
\theta_2 \approx 39.5°
\]

Therefore, the angle of refraction is approximately **39.5°**.

The correct answer is **39.5°**.