A beam with wavelength falls on a stack of partially reflecting p… - Vidyadip

MCQ

A beam with wavelength $\lambda$ falls on a stack of partially reflecting planes with separation d. The angle $\theta$ that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where $n =1, 2, ……$)

A
${\sin ^{ - 1}}\left( {\frac{{n\lambda }}{d}} \right)$
B
${\tan ^{ - 1}}\left( {\frac{{n\lambda }}{d}} \right)$
✓
${\sin ^{ - 1}}\left( {\frac{{n\lambda }}{{2d}}} \right)$
D
${\cos ^{ - 1}}\left( {\frac{{n\lambda }}{{2d}}} \right)$

✓

Answer

Correct option: C.

${\sin ^{ - 1}}\left( {\frac{{n\lambda }}{{2d}}} \right)$

c
(c) Path difference $ = 2d\sin \theta $
$\therefore $ For constructive interference
$2d\sin \theta = n\lambda $
$ \Rightarrow \theta = {\sin ^{ - 1}}\left( {\frac{{n\lambda }}{{2\,d}}} \right)$

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