Question

A parallel beam of light $(\lambda =500nm)$ is incident at an angle $\alpha ={30}^o$ with the normal to the slit plane in Young's double-slit experiment. Assume that the intensity due to each slit at any point on the scree is $I_0$. Point $O$ is equidistant from $S_1$ and $S_2$. The distance between slits is $1mm$. Then

• A. the intensity at $O$ is $I_0$
• B. the intensity at $O$ is zero
• C. the intensity at a point on the screen $1m$ below $O$ is $I_0$
• D. the intensity at a point on the screen $1m$ below $O$ is zero

Answer 1

Answer: (A), (C)

the intensity at $O$ is $I_0$
the intensity at a point on the screen $1m$ below $O$ is $I_0$

$IntensityatOd\sin \alpha =n\lambda {10}^{-3}\sin 30=500n\times {10}^{-9}n=1000\Rightarrow Constructiveinterferenceoccurs1mbelowO-d\sin \alpha +dsin\theta =n\lambda \tan \theta =\frac{1}{\sqrt{3}}n=0\Rightarrow Constructiveinterferenceoccurs$