Question

14.) find the angle of refraction, 0 < θ₂ < 90°, if θ₁ = 45°, n₁ = 1.000 (air), and n₂ = 1.333 (water). round to the nearest degree.
snell’s law
n₁ sinθ₁ = n₂ sinθ₂

Explanation:

Step1: Recall Snell's Law

Snell's Law is given by \( n_1 \sin\theta_1 = n_2 \sin\theta_2 \). We need to solve for \( \theta_2 \).

Step2: Substitute known values

We know \( n_1 = 1.000 \), \( \theta_1 = 45^\circ \), and \( n_2 = 1.333 \). Substitute these into the formula:
\( 1.000 \times \sin(45^\circ) = 1.333 \times \sin\theta_2 \)

Step3: Solve for \( \sin\theta_2 \)

First, calculate \( \sin(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.7071 \). Then:
\( \sin\theta_2 = \frac{1.000 \times \sin(45^\circ)}{1.333} = \frac{0.7071}{1.333} \approx 0.5305 \)

Step4: Find \( \theta_2 \)

Take the inverse sine (arcsin) of 0.5305:
\( \theta_2 = \arcsin(0.5305) \approx 32^\circ \) (rounded to the nearest degree)

Answer:

\( 32^\circ \)