(b)i. Explain what is meant by the statement: the refractive index of glass is 1.5.
ii. Calculate the critical angle of a medium of refractive index 1.65 when light passes from the medium to air.
Principle: This is the prism refraction experiment. For each angle of incidence i the emergent angle e is measured, and \( \phi = i + e \) is evaluated. The angle of deviation \( \theta \) is plotted against \( \phi \); the graph passes through a minimum deviation, and reading the slope and intercept confirms the relation between the angles for the equilateral prism.
Method (as instructed): Trace the outline ABC of the prism, draw the incident ray MN at i = 5 degrees to the normal at N on AB, fix pins P1 and P2, replace the prism, then sight through BC and fix pins P3 and P4 in line with the images of P1 and P2. Remove the prism, join P4 P3, produce it to Q on BC and to P, draw the normal at Q, and measure \( \theta \) and e. Repeat for i = 10, 15, 20, 25 degrees, tabulate, and plot \( \theta \) against \( \phi = i + e \).
Two precautions:
- Fix the pins vertically and well spaced apart, and view their images with one eye to line them up accurately.
- Use a sharp pencil for tracing and mark the pin positions precisely to reduce error.
(b)(i) "The refractive index of glass is 1.5" means that the speed of light in a vacuum (or air) is 1.5 times its speed in the glass; equivalently, for light passing from air into the glass, \( \dfrac{\sin i}{\sin r} = 1.5 \).
(b)(ii) Critical angle for a medium of refractive index 1.65: \[ \sin C = \dfrac{1}{n} = \dfrac{1}{1.65} = 0.6061, \qquad C = 37.3^\circ. \]