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°

1 answer

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°.