Question

A parallel beam of light $\lambda =5000\stackrel{o}{A}$ is incident at an angle $\theta ={30}^o$ with the normal of the slit in a YDSE. Intensity due to each slit is $I_o.$ Point O is equidistance from $S_1$ and $S_2.$ Distance between slits is 1 mm, then

• A. Intensity at 0 is $4I_o$
• B. Intensity at 0 is $2I_o$
• C. Intensity at point 2 mm above 0 is $4I_o$
• D. Intensity at point 3 mm above 0 is zero

Answer 1

Answer: (A), (C)

The correct options are
A Intensity at 0 is $4I_o$
C Intensity at point 2 mm above 0 is $4I_o$

$△x=d\sin \theta =\frac{d}{2}=\frac{1}{2}mm=0.5mm$
since $\lambda =5000\stackrel{o}{A}$
So $\Delta x=n\lambda$ where $n$ is integer.
So at O, we get constructive interference, hence $4I_o$ intensity.

Fringe width $w=\frac{\lambda D}{d}=\frac{5000\times {10}^{-10}\times 2}{1\times {10}^{-3}}=1mm$
So we get $4I_o$ intensity at 1, 2, 3,...$n$ $mm$ from 0 where $n$ is an integer.