AP Physics 2 Exam Question:

A laser beam with a wavelength of 532 nm is incident on a glass block at an angle of 30° with respect to the normal. The refractive index of the glass is 1.5.

(a) Determine the angle of refraction as the laser beam enters the glass block.

(b) After entering the glass block, the laser beam encounters a second medium with a refractive index of 1.2. Calculate the angle of refraction as the laser beam exits the glass block and enters the second medium.

(c) Calculate the critical angle for total internal reflection to occur between the glass block and the second medium.

Answer:

(a) To find the angle of refraction as the laser beam enters the glass block, we can use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media:

n1 * sin(θ1) = n2 * sin(θ2)

where n1 and n2 are the refractive indices of the first and second media respectively, and θ1 and θ2 are the angles of incidence and refraction.

Given: Wavelength (λ) = 532 nm = 532 x 10^-9 m Angle of incidence (θ1) = 30° Refractive index of glass (n1) = 1.5

First, convert the wavelength into meters:

λ = 532 x 10^-9 m

Now, we can calculate the angle of refraction using Snell's Law:

n1 * sin(θ1) = n2 * sin(θ2)
1.5 * sin(30°) = n2 * sin(θ2)
1.5 * (1/2) = n2 * sin(θ2)
0.75 = n2 * sin(θ2)
sin(θ2) = 0.75 / n2

Since we want to find the angle of refraction (θ2), we can use the arcsin function to calculate it:

θ2 = arcsin(0.75 / n2)

Substituting the value of n2 (refractive index of air = 1) into the equation:

θ2 = arcsin(0.75 / 1)
θ2 = arcsin(0.75)
θ2 ≈ 48.59°

Therefore, the angle of refraction as the laser beam enters the glass block is approximately 48.59°.

(b) To calculate the angle of refraction as the laser beam exits the glass block and enters the second medium, we can again use Snell's Law:

n2 * sin(θ2) = n3 * sin(θ3)

Given: Refractive index of the second medium (n3) = 1.2

Now, we can calculate the angle of refraction using the updated Snell's Law equation:

n2 * sin(θ2) = n3 * sin(θ3)
1 * sin(48.59°) = 1.2 * sin(θ3)
sin(48.59°) / 1.2 = sin(θ3)
sin(θ3) ≈ 0.717

Therefore, the angle of refraction as the laser beam exits the glass block and enters the second medium is approximately arcsin(0.717) ≈ 46.96°.

(c) To calculate the critical angle (θc) for total internal reflection between the glass block and the second medium, we can use the equation:

θc = arcsin(n3 / n1)

Given:
Refractive index of the second medium (n3) = 1.2
Refractive index of the glass (n1) = 1.5

Now, we can calculate the critical angle using the equation:

θc = arcsin(n3 / n1) θc = arcsin(1.2 / 1.5) θc = arcsin(0.8) θc ≈ 53.13°

Therefore, the critical angle for total internal reflection to occur between the glass block and the second medium is approximately 53.13°.

Hence, we have determined the angle of refraction as the laser beam enters the glass block, exits the glass block and enters the second medium, and also the critical angle for total internal reflection.