Question

an incident ray of light strikes water at an angle of 30° the index of refraction of air is 1.0003, and the index of refraction of water is 1.33. what is the angle of refraction rounded to the nearest whole number? 22° 24° 30° 42°

Explanation:

Step1: Apply Snell's Law

Snell's Law is given by \(n_1\sin\theta_1 = n_2\sin\theta_2\), where \(n_1\) is the refractive index of the incident medium (air, \(n_1 = 1.0003\)), \(\theta_1\) is the angle of incidence (\(\theta_1=30^{\circ}\)), \(n_2\) is the refractive index of the refracting medium (water, \(n_2 = 1.33\)), and \(\theta_2\) is the angle of refraction.
Substituting the values into Snell's Law: \(1.0003\times\sin(30^{\circ})=1.33\times\sin\theta_2\).
Since \(\sin(30^{\circ})=\frac{1}{2}\), the equation becomes \(1.0003\times\frac{1}{2}=1.33\times\sin\theta_2\), or \(\sin\theta_2=\frac{1.0003}{2\times1.33}\).

Step2: Calculate \(\sin\theta_2\)

\(\sin\theta_2=\frac{1.0003}{2.66}\approx0.376\).

Step3: Find \(\theta_2\)

Using the inverse - sine function, \(\theta_2=\sin^{- 1}(0.376)\approx22^{\circ}\) (rounded to the nearest whole number).

Answer:

A. \(22^{\circ}\)