Final answer:
The maximum value of the angle of incidence to avoid total internal reflection when light speed doubles is just below 30 degrees; the closest provided option is C. 30 degrees.
Step-by-step explanation:
When a ray of light moves from one medium to another, its speed changes.
If the light enters a medium where its speed doubles, this implies that the second medium has a lower optical density compared to the first.
According to Snell's law, the relationship between the angles of incidence and refraction is given by n1*sin(θ1) = n2*sin(θ2), where n1 and n2 are the refractive indices of the first and second media, respectively, and θ1 and θ2 are the angles of incidence and refraction.
For total internal reflection to occur, the angle of incidence must be greater than the critical angle, θc.
The critical angle can be found using the refractive indices: sin(θc) = n2/n1.
If the velocity of light doubles, then n2 = n1/2. Therefore, sin(θc) = 1/2, which means θc = 30°.
Thus, for total internal reflection to not occur, the angle of incidence must be less than the critical angle, so the maximum value of the angle of incidence is just below 30°.
The correct answer to the student's question is C. 30°, as this is the value of the critical angle beyond which total internal reflection would occur in this situation.