Consider a Young’s double slit experiment as shown in figure. Wha… - Vidyadip

MCQ

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation $d$ in terms of wavelength $\lambda $ such that the first minima occurs directly in front of the slit $(S_1)$?

✓
$\frac{\lambda }{{2\left( {\sqrt 5 - 2} \right)}}$
B
$\frac{\lambda }{{\left( {\sqrt 5 - 2} \right)}}$
C
$\frac{\lambda }{{2\left( {5 - \sqrt 2 } \right)}}$
D
$\frac{\lambda }{{\left( {5 - \sqrt 2 } \right)}}$

✓

Answer

Correct option: A.

$\frac{\lambda }{{2\left( {\sqrt 5 - 2} \right)}}$

a
$\sqrt{(2 d)^{2}+(d)^{2}}-2 d=\frac{\lambda}{2}$

$\Rightarrow \quad(\sqrt{5}-2) d=\frac{\lambda}{2}$

$\Rightarrow \quad d=\frac{\lambda}{2(\sqrt{5}-2)}$

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