A beamsplitter divides monochromatic light of vacuum wavelength into two beams which…
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Interference and diffraction
Optics and Photonics, Ch Harmonic waves, phasors and group velocity
Problem
A beamsplitter divides monochromatic light of vacuum wavelength 500nm into two beams which then travel routes of equal geometric length in air to a small detector, where they recombine with a fixed phase difference. A thin slab of transparent plastic of refractive index n=1.50 and thickness d=4.50μm is then inserted in beam 2, normal to the beam, so that it replaces an equal thickness of air. Ignore reflection losses at the faces of the slab and any change of the beam direction, and take the index of air as 1.00 and c=3.00×108ms−1. Measured separately at the detector, beam 1 has irradiance I1 and beam 2 has irradiance I1/9; irradiance is proportional to the square of the field amplitude.
((a)) Find the frequency of the light and its wavelength inside the slab.
((b)) Find the phase difference δ introduced between the two routes by the slab, in radians.
((c)) Taking beam 1 to have amplitude E1, use phasor addition to find the resultant amplitude at the detector as a multiple of E1, and the resultant irradiance as a multiple of I1.