Question

14.) find the angle of refraction, ( 0 < \theta_2 < 90^circ ), if ( \theta_1 = 45^circ ), ( n_1 = 1.000 ) (air), and ( n_2 = 1.333 ) (water). round to the nearest degree.
snell’s law
( n_1 sin\theta_1 = n_2 sin\theta_2 )

Explanation:

Step1: Recall Snell's Law

Snell's Law is \( n_1 \sin\theta_1 = n_2 \sin\theta_2 \). We need to solve for \( \theta_2 \). Given \( n_1 = 1.000 \), \( \theta_1 = 45^\circ \), \( n_2 = 1.333 \).

Step2: Rearrange the formula

From \( n_1 \sin\theta_1 = n_2 \sin\theta_2 \), we get \( \sin\theta_2=\frac{n_1 \sin\theta_1}{n_2} \).

Step3: Substitute the values

Substitute \( n_1 = 1.000 \), \( \sin\theta_1=\sin45^\circ=\frac{\sqrt{2}}{2}\approx0.7071 \), \( n_2 = 1.333 \) into the formula:
\( \sin\theta_2=\frac{1.000\times0.7071}{1.333}\approx\frac{0.7071}{1.333}\approx0.5304 \)

Step4: Find \( \theta_2 \)

Take the inverse sine: \( \theta_2=\arcsin(0.5304)\approx32^\circ \) (rounded to the nearest degree).

Answer:

\( 32^\circ \)