Question:

A light ray travelling in air with an angle of incidence of 30° strikes a transparent medium with an index of refraction of 1.5. The ray undergoes both reflection and refraction at the interface between the two media. Given that the speed of light in air is 3.0 x 10^8 m/s, determine:

a) The angle of reflection.

b) The angle of refraction.

Answer:

a) To determine the angle of reflection, we can use the law of reflection which states that the angle of incidence is equal to the angle of reflection. The angle of incidence is given as 30°, so the angle of reflection is also 30°.

b) To determine the angle of refraction, we can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media. The equation for Snell's law is:

n1 * sin(θ1) = n2 * sin(θ2)

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

In this case, n1 is the index of refraction of air, which is 1.0 since we are given that the light ray is travelling in air. n2 is the index of refraction of the transparent medium, which is given as 1.5. θ1 is the angle of incidence, which is given as 30°.

Substituting the values into Snell's law, we have:

1.0 * sin(30°) = 1.5 * sin(θ2)

Taking the sine of 30°, we get:

sin(30°) ≈ 0.5

Substituting this value back into the equation, we have:

1.0 * 0.5 = 1.5 * sin(θ2)

Simplifying the equation, we find:

0.5 = 1.5 * sin(θ2)

Dividing both sides of the equation by 1.5, we have:

0.5 / 1.5 = sin(θ2)

Simplifying further, we get:

sin(θ2) ≈ 0.33

To find θ2, we take the inverse sine (or arcsine) of 0.33 using a calculator:

θ2 ≈ arcsin(0.33)

Using a calculator, we find:

θ2 ≈ 19.47°

Therefore, the angle of refraction is approximately 19.47°.

In summary, the answer to the given problem is:

a) Angle of reflection = 30° b) Angle of refraction ≈ 19.47°