A narrow slit source is held in a still pool of water ( ) at a depth mm below the…
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Polarisation and anisotropic media · Interference and diffraction
Optics and Photonics, Ch Two-beam interference and interferometry
Problem
A narrow slit source S is held in a still pool of water (n=1.33) at a depth h=1.0 mm below the flat surface. A screen stands in the water a distance L=1.0 m away, reaching up to the surface. Light from S reaches the screen either directly or after reflecting from the underside of the water surface, and the arrangement is unfolded and analysed exactly like the standard Lloyd's mirror, with the water surface playing the role of the mirror. The light is s-polarised.
((a)) A reflected ray meeting the surface at 20∘ from the normal: is that below the critical angle for the water-air interface, and does the reflection there add a phase?
((b)) Predict whether the fringe at the point where the screen meets the surface (zero path difference) is bright or dark, and justify your reasoning.
((c)) How far below the surface must a point on the screen lie before the ray reflected to it meets the surface below the critical angle?