AP Physics 2 Exam Question

A ray of light is incident on a glass slab. The angle of incidence is 40 degrees and the index of refraction for the glass is 1.5. Find:

a) The angle of refraction at the glass-air interface. b) The angle of refraction at the air-glass interface. c) The speed of light in the glass. d) The critical angle for total internal reflection.

Assume the speed of light in air is 3.00 × 10^8 m/s.

Answer

a) The angle of refraction at the glass-air interface can be calculated using Snell's law:

n1 * sin(theta1) = n2 * sin(theta2),

where n1 is the refractive index of the medium of incidence (air) and n2 is the refractive index of the medium of refraction (glass).

Given: n1 = 1 (since the medium is air), theta1 = 40 degrees, and n2 = 1.5.

We can rearrange the equation to solve for theta2:

sin(theta2) = (n1 / n2) * sin(theta1)

sin(theta2) = (1 / 1.5) * sin(40)

sin(theta2) = 0.6667 * 0.6428

sin(theta2) = 0.4284

Now, we find the inverse sine of 0.4284 to get theta2:

theta2 = sin^(-1)(0.4284) ≈ 26.11 degrees

Therefore, the angle of refraction at the glass-air interface is approximately 26.11 degrees.

b) The angle of refraction at the air-glass interface is equal to the angle of incidence at the glass-air interface. Therefore, the angle of refraction at the air-glass interface is also approximately 26.11 degrees.

c) The speed of light in a medium can be calculated using the formula:

v = c / n,

where v is the speed of light in the medium, c is the speed of light in vacuum (approximately 3.00 × 10^8 m/s), and n is the refractive index of the medium.

Given: c = 3.00 × 10^8 m/s and n = 1.5.

Substituting the values into the formula:

v = (3.00 × 10^8 m/s) / 1.5

v = 2.00 × 10^8 m/s

Therefore, the speed of light in the glass is approximately 2.00 × 10^8 m/s.

d) The critical angle for total internal reflection can be calculated using the formula:

theta_critical = sin^(-1)(n2 / n1),

where n1 is the refractive index of the medium of incidence (air) and n2 is the refractive index of the medium of refraction (glass).

Given: n1 = 1 (since the medium is air) and n2 = 1.5.

Substituting the values into the formula:

theta_critical = sin^(-1)(1.5 / 1)

theta_critical = sin^(-1)(1.5)

Using a calculator, we find:

theta_critical ≈ 41.8 degrees

Therefore, the critical angle for total internal reflection is approximately 41.8 degrees.