During a laboratory experiment a student wishes to determine the refractive index of a prism material by measuring the deviation of a narrow light beam.
a. (i) Starting from the result d≈(μ−1)A valid for small apex angles, show algebraically how the refractive index μ may be obtained from the measured deviation d and the known apex angle A. No numerical substitution is required in this part.
b. (ii) The student uses a thin prism of apex angle 2∘ and measures a deviation of 1.2∘ for a particular monochromatic light. Calculate the refractive index of the prism material for this wavelength.
c. (iii) If another prism of the same material but of apex angle 4∘ is used under identical conditions, predict the deviation produced. State any approximation you make.