Question

A ray of light travels from air to glass. The incident ray makes an angle of 45 degrees while the refracted ray makes and angle of 30 degrees with the normal to the interface. The speed of light in air is 3.0×108m/s. What is the of speed of light in glass?

A. 2.12×108m/s
B. 4.24×108m/s
C. 3.73×108/s
D. 3.00×108$/s

Answer 1

Answer on Question 33267, Physics, Optics

Question:

A ray of light travels from air to glass. The incident ray makes an angle $45{}^{\circ}$ while the refracted ray makes an angle of $30{}^{\circ}$ with the normal to the interface. The speed of light in air is $3.0 \cdot 10^{8} \, \text{m/s}$. What is the speed of light in glass?

a) $2.12 \cdot 10^{8} \, \text{m/s}$

b) $4.24 \cdot 10^{8} \, \text{m/s}$

c) $3.73 \cdot 10^{8} \, \text{m/s}$

d) $3.0 \cdot 10^{8} \, \text{m/s}$

Solution:

From the Snell’s law we have:

$$\frac{\sin \theta_1}{\sin \theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2},$$

where, $\theta_1 = 45{}^{\circ}$ is the angle of incidence, $\theta_2 = 30{}^{\circ}$ is the angle of refraction, $v_1$ is the speed of light in air, $v_2$ is the speed of light in glass, $n_1$ is the refractive index of air, $n_2$ is the refractive index of glass.

Thus, we can find the speed of light in glass:

$$v_2 = v_1 \frac{\sin \theta_2}{\sin \theta_1} = 3.0 \cdot 10^{8} \, \frac{\text{m}}{\text{s}} \cdot \frac{\sin 30{}^{\circ}}{\sin 45{}^{\circ}} = 3.0 \cdot 10^{8} \, \frac{\text{m}}{\text{s}} \cdot \frac{0.5}{0.707} = 2.12 \cdot 10^{8} \, \frac{\text{m}}{\text{s}}.$$

Answer:

a) $2.12 \cdot 10^{8} \, \frac{\text{m}}{\text{s}}$.

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