(a) The figure at the right shows a cross-sectional end view of a thick-walled hollow cylindrical tube with inner radius r and outer radius R, made of glass having index of refraction n. Assume that r < R/n.
The light ray ABC in the diagram (together with the parallel ray shown coming from the axis of the cylindrical tube) defines the apparent internal radius r* as perceived by someone observing from outside the tube.
(i) Use Snell's law to derive a formula for r* in terms of R, n, and r.
(ii) What would happen if, contrary to our assumption above, r were greater than R/n? (Hint: Think about the behavior of the light ray ABC.)
(b) White light, containing all wavelengths 400 nm to 700 nm, shines perpendicularly on the front of a thin, vertical film of refractive index 1.30 and thickness 800 nm in air, as shown in edge view in the sketch at the right. Taking interference effects into account,
(i) Which wavelength(s) will be most noticeable to an observer in front of the film?
(ii) Which wavelength(s) will be most noticeable to an observer behind the film?