Question

In a Young's double slit experiment, light with $\lambda =$ 546 nm is used. The first order maximum is found to be at 2.5${}^{\circ }$. The slit separation is:

• A. 12.5 $\mu m$
• B. 1.25 $\mu m$
• C. 125 $mm$
• D. 125 $\mu m$

Answer 1

Answer: (A)

12.5 $\mu m$

For interference in YDSE
$dsin\theta =n\lambda$
For $I^{st}$ order maxima $n=1$
$So,dsin\theta =\lambda$
$d=\frac{\lambda }{sin\theta }$
$d=\frac{\lambda }{\theta }$ ($\because \theta$ is very small sin $\theta \simeq \theta$)
$=\frac{546\times {10}^{-9}}{\frac{{2.5}^{\circ }\times 3.14}{{180}^{\circ }}}(\because {180}^{\circ }=3.14radian)$
$=12500\times {10}^{-9}$
$=12.5\times {10}^{-6}m$
$=12.5\mu m$