Question

A beam of light in air strikes a slab of glass (n = 1.51) and is partially reflected and partially refracted. Part A Determine the angle of incidence if the angle of reflection is twice the angle of refraction. Express your answer using three significant figures.

Answer 1

To determine the angle of incidence when the angle of reflection is twice the angle of refraction, we can use the laws of reflection and refraction. By applying Snell's law and the given refractive indices, we can solve for the angle of incidence.

Step-by-step explanation:

To determine the angle of incidence when the angle of reflection is twice the angle of refraction, we can use the laws of reflection and refraction. According to the laws of reflection, the angle of incidence is equal to the angle of reflection, while according to Snell's law, the angle of refraction is related to the angle of incidence and the refractive indices of the two mediums involved. Let's represent the angle of incidence as ₁, the angle of reflection as ₂, and the angle of refraction as ₃. Since ₂ is twice ₃, we have ₂ = 2₃. Additionally, we know that the refractive index of air is approximately 1.00 and the refractive index of glass is 1.51. By applying Snell's law and the given information, we can solve for ₁:

Sin(₁) = Sin(₃) * (n₂ / n₁)

Sin(₁) = Sin(₂ / 2) * (n₂ / 1.00)

Now, we can plug in the values and solve for ₁:

Sin(₁) = Sin(₂ / 2) * (1.51 / 1.00)

Sin(₁) = Sin(₂ / 2) * 1.51

Sin(₁) = Sin(2₃ / 2) * 1.51