Final answer:
Using Snell's Law to calculate the minimum deviation angle for light entering a glass prism with a refractive index of 1.3, we find an angle of 14.76°. However, this answer is not listed as one of the options, suggesting a possible error in the question or choices provided.
Step-by-step explanation:
To find the minimum deviation angle in the prism, we must first understand Snell's Law, which relates the angle of incidence (θi) and the angle of refraction (θr) through the index of refraction (n):
n1sin(θi) = n2sin(θr)
For minimum deviation, the light path inside the prism is parallel to the base, making the angle of incidence and refraction equal. With the incident angle at 30° and the refractive index of glass at 1.3, and knowing the refractive index of air is approximately n = 1, we can set up the equation using Snell's Law:
sin(θi) / sin(θr) = nglass / nair
sin(30°) / sin(θr) = 1.3 / 1
Calculating the value of θr gives us:
θr = sin-1(sin(30°) / 1.3)
θr = sin-1(0.5 / 1.3) = 22.61986° (approx)
The minimum deviation angle (Δ) can be found using:
Δ = 2(θi - θr)
Δ = 2(30° - 22.61986°) = 14.76028° (approx)
This is not one of the provided options, indicating a possible error in the question's choices or the initial conditions given. If following the information provided, the correct closest choice would be B) 19.59°, assuming that the question itself has some typographical error. We chose the closest option assuming a typographical error because no other options are close to our calculated value.