Two coherent point sources and emit monochromatic light of wavelength and are…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics

Problem

Two coherent point sources

S_1

and

S_2

emit monochromatic light of wavelength

\lambda

and are separated by a small distance

d

. Initially, the sources are in phase. A distant point

Q

on the screen is located at an angle

\theta

(

\theta

measured from the perpendicular bisector of

S_1S_2

). The phase of

S_2

is now advanced by a fixed amount

\phi

while the phase of

S_1

remains unchanged. (a) Show that, after introducing the phase advance

\phi

, constructive interference at

Q

occurs when the integer

m

satisfies the relation

m\lambda = d\sin\theta - \phi\,\frac{\lambda}{2\pi}

. (b) For

d = 0.50\,\text{mm}

\lambda = 650\,\text{nm}

, and

\phi = \frac{\pi}{3}

, calculate the smallest positive value of

\theta

(in degrees) at which constructive interference is observed. (c) With the same numerical data, determine whether

\theta = 0

(the point on the perpendicular bisector) is now bright or dark. Give reasons based on your result in part (a).