A horizontally oriented transparent slab of uniform thickness d=1.20cm is placed in air. A fast electronic photodetector measures a time delay Δt=2.0×10−11s between a laser pulse that travels through the slab and an otherwise identical pulse that travels the same geometric distance entirely in air. The pulses enter the slab at normal incidence.
Using the information provided, address the tasks below. Show all symbolic work before substituting numerical values.
(a) Derive an algebraic expression for the speed v of light in the slab in terms of c, d, and Δt.
(b) Calculate the numerical value of the slab’s index of refraction.
(c) The slab is now submerged in water (index 1.33). A laser beam in the water approaches the slab at an angle of 30∘ with respect to the normal. Determine the angle of the beam inside the slab with respect to the normal.
(d) Discuss whether total internal reflection can occur at the water–slab interface when light attempts to pass from the slab back into the water. Support your answer quantitatively.