Final answer:
To achieve total internal reflection in an efficient corner reflector with air outside and an incident angle of 45.0°, the material's minimum index of refraction must be 1.41. This is calculated using Snell's Law, where the critical angle is equal to the incident angle and the refractive index of air is approximately 1.00.
Step-by-step explanation:
To determine the minimum index of refraction for a material used in a corner reflector employing total internal reflection, we rely on the relationship between the incident angle and the critical angle of the material. For total internal reflection to occur, the incident angle must be greater than the critical angle when light tries to move from a medium with a higher refractive index to a medium with a lower one, such as from a solid to air.
Since air has a refractive index close to 1 and the incident angle is given as 45.0°, we need the critical angle to be at least equal to 45.0° for total internal reflection to occur.
Using Snell's Law, which is the equation n₁ sin(θ₁) = n₂ sin(θ₂), where n₁ is the refractive index of the first medium, θ₁ is the incident angle, n₂ is the refractive index of the second medium (air, in this case, with approximately 1.00), and θ₂ is 90°, since it's the critical angle for total internal reflection, we can isolate for n₁ leading to n₁ = 1/sin(θ₁).
For an incident angle of 45.0°, the minimum index of refraction (n₁) we calculate is 1/sin(45.0°), which is roughly 1.41.
Thus, the correct answer would be option (b) 1.41 as the minimum index of refraction of the material for the corner reflector.