Question

light travels from air into glass at an incident angle of 40.8°. if the light refracts at an angle of 25.8°, what is the refractive index of the glass?

Explanation:

Identify the given values

We are given the following values from the problem statement:

• Medium 1 is air, which has a known refractive index:

\(n_1 \approx 1.00\)

• The angle of incidence in air:

\(\theta_1 = 40.8^\circ\)

• The angle of refraction in glass:

\(\theta_2 = 25.8^\circ\)

State the governing physical law

To find the refractive index of glass (\(n_2\)), we use Snell's Law, which relates the indices of refraction of two media to the angles of incidence and refraction:

$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$

Rearrange the formula for the unknown

We solve the equation for the refractive index of the second medium, \(n_2\):

$$n_2 = \frac{n_1 \sin(\theta_1)}{\sin(\theta_2)}$$

Substitute the values and calculate

Substitute the given values into the rearranged equation:

$$n_2 = \frac{1.00 \cdot \sin(40.8^\circ)}{\sin(25.8^\circ)}$$

Calculate the sine values:

• \(\sin(40.8^\circ) \approx 0.6534\)
• \(\sin(25.8^\circ) \approx 0.4352\)

Now, perform the division:

$$n_2 \approx \frac{0.6534}{0.4352} \approx 1.50$$

Answer:

\(1.50\)