In the figure shown S is a point monochromatic light source of frequency `6xx10^(14)Hz`.M is a concave mirror of radius of curvature 20 cm and L is a thin converging lens of focal length 3.75 cm AB is the principal axis of M and L.
Light reflected from the mirror and refracted from the lens in succession reaches the screen. An interference pattern is obtained on the screen by this arrangement.
Q. Distance between two coherent sources whichmakes interference pattern on the screen is

Options

A. 1 mm
B. 0.5 mm
C. 1.5 mm
D. 0.25 mm

Answer

B

Explanation

Wavelength of light `lamda=(c)/(f)=5xx10^(-7)m`
image formed by M: `(1)/(v)+(1)/(-30)=(1)/(-10)impliesv=-15` cm also `M=-(v)/(u)=-(-15)/(-30)=-(1)/(2)`
This will be located at 15 cm left of M and 0.5 mm above the line AB.
This will act as an object for the lens L.
Now for the lens `u=-7.5cm ` and `m=(v)/(u)=(7.5)/(-7.5)=-1`
So it will be at 7.5 cm to the left of L and 0.5 mm below line AB. see the ray diagram second image `I_(2)` and source S will act as two slits (as im YDSE) to produce the interference pattern. distance between them =0.5 mm(=d)