Question

In Young's double slit experiment,the angular position of a point on the central maxima whose intensity is one fourth of maximum intensity

• A. ${\sin }^{-1}\left(\lambda /d\right)$
• B. ${\sin }^{-1}\left(\lambda /2d\right)$
  
• C. ${\sin }^{-1}\left(\lambda /3d\right)$
  
• D. ${\sin }^{-1}\left(\lambda /4d\right)$
  

Answer 1

The correct option is C ${\sin }^{-1}\left(\lambda /3d\right)$

Intensity at a point with path difference $\varphi$ is given by $I=I_{0}co{s}^2\frac{\varphi }{2}$

$⟹\frac{I_0}{4}=I_{0}co{s}^2\frac{\varphi }{2}$
$⟹\varphi =\frac{2\pi }{3}$

Thus path difference between light rays at the point$=\frac{\lambda }{2\pi }\times \frac{2\pi }{3}$

$=\frac{\lambda }{3}$

$⟹sin\theta =\frac{y}{D}=\frac{\lambda }{3d}$