Question

# Coherent light with wavelength λ passes through narrow slits separated by a distance d, producing an...

Coherent light with wavelength λ passes through narrow slits separated by a distance d, producing an interference pattern on a distant screen. Suppose, however, that one slit allows a little more light through so that the amplitudes of the electric field for the waves are not equal when they arrive at the screen. Instead, the electric fields are given by

E 1 ( t ) = 3 E 0 cos ⁡ ( ω t )
E 2 ( t ) = 4 E 0 cos ⁡ ( ω t + ϕ )

where ϕ is the phase difference due to the path difference from the slits to the point on the screen.

a) Draw the phasor diagram for the central maximum, and find the amplitude of the resultant electric field as a multiple of E 0.

b) Draw the phasor diagram for an intensity minimum, and find the amplitude of the resultant electric field as a multiple of E 0.

c) Draw the phasor diagram for a point P on the screen. The location of point P is such that ϕ = π / 2. Find the amplitude of the resultant electric field as a multiple of E 0.

d) If the intensity of the central maximum of I 0, what is the intensity at (i) an intensity minimum and (ii) point P?