The angle of incidence for which the angle of refraction is twice the angle of incidence is approximately 36.87 degrees.
Let's denote the angle of incidence as 'i' and the angle of refraction as 'r'. We are given that the refractive index of glass is 1.6 and the angle of refraction is twice the angle of incidence, which can be expressed as:
r = 2i
According to Snell's law of refraction, the refractive index of a medium is related to the angles of incidence and refraction by the following equation:
n1 * sin(i) = n2 * sin(r)
Since the light is passing from glass to air, n1 = 1.6 and n2 = 1. Substituting the given values and the expression for r into Snell's law, we get:
1.6 * sin(i) = 1 * sin(2i)
Using the double-angle formula for sine, sin(2i) = 2sin(i)cos(i), we can rewrite the equation as:
1.6 * sin(i) = 2sin(i)cos(i)
Dividing both sides by sin(i), we get:
1.6 = 2cos(i)
Solving for cos(i), we find:
cos(i) = 0.8
Taking the inverse cosine of both sides, we obtain:
i = cos^(-1)(0.8)
i ≈ 36.87°
Therefore, the angle of incidence for which the angle of refraction is twice the angle of incidence is approximately 36.87 degrees.