To determine the angle of refraction when light travels from air into glass, we need to apply Snell's Law. The refractive indices of air and glass are provided, as is the initial angle of incidence in the air.
Given data:
- Refractive index of air, [tex]\(n_1 = 1.00\)[/tex]
- Angle of incidence, [tex]\(\theta_1 = 35^{\circ}\)[/tex]
- Refractive index of glass, [tex]\(n_2 = 1.50\)[/tex]
The equation for Snell's Law is:
[tex]\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\][/tex]
To find the angle of refraction [tex]\(\theta_2\)[/tex] in the glass, we rearrange the equation:
[tex]\[
\sin(\theta_2) = \frac{n_1 \sin(\theta_1)}{n_2}
\][/tex]
Next, we need to perform the calculations step-by-step:
1. Convert the angle of incidence from degrees to radians:
[tex]\[
\theta_1 = 35^{\circ} \quad \Rightarrow \quad \theta_1 = \text{radians}(35^{\circ}) = \frac{35 \pi}{180} \approx 0.6109 \text{ radians}
\][/tex]
2. Calculate the sine of the angle of incidence:
[tex]\[
\sin(35^{\circ}) = \sin(0.6109) \approx 0.5736
\][/tex]
3. Substitute the values into the equation:
[tex]\[
\sin(\theta_2) = \frac{1.00 \times 0.5736}{1.50} = \frac{0.5736}{1.50} \approx 0.3824
\][/tex]
4. Find the angle that corresponds to this sine value by taking the inverse sine:
[tex]\[
\theta_2 = \sin^{-1}(0.3824) \approx 22.48^{\circ}
\][/tex]
The closest option to [tex]\(22.48^{\circ}\)[/tex] given in the choices is [tex]\(22.5^{\circ}\)[/tex].
Thus, the correct answer is:
C. [tex]\(22.5^{\circ}\)[/tex]
