A ray of light in air strikes a glass plate (n = 1.50) at an incidence angle of 50 degrees. Determine the angles of the reflected and transmitted rays.

Answer 1

To determine the angle of the reflected ray, we can use the law of reflection, which states that the angle of incidence is equal to the angle of reflection. Thus, the angle of the reflected ray is 50 degrees.

To determine the angle of the transmitted ray, we can use Snell's law, which states that:

n1 * sinθ1 = n2 * sinθ2

where n1 and n2 are the indices of refraction for the two materials (air and glass in this case), and θ1 and θ2 are the angles of incidence and transmission, respectively. In this problem, n1 = 1.00 (air), n2 = 1.50 (glass), and θ1 = 50 degrees. We can rearrange the formula and solve for θ2:

sinθ2 = (n1 * sinθ1) / n2

Plugging in the values from the problem:

sinθ2 = (1.00 * sin(50°)) / 1.50
sinθ2 ≈ 0.514

Now find the angle θ2:

θ2 = arcsin(0.514)
θ2 ≈ 31.1°

So, the angle of the transmitted ray in the glass is approximately 31.1 degrees.