First slide

Coherent sources and their importance in interference

Question

Consider an YDSE that has different slits width. As a result, amplitudes of waves from two slits are A and 2A, respectively. If $I_{0}$ be the maximum intensity of the interference pattern, then intensity of the pattern at a point where phase difference between waves is , is

Moderate

A

$I_{0} \cos^{2} ϕ$
B

$\frac{I_{0}}{3} \sin^{2} \frac{ϕ}{2}$
C

$\frac{I_{0}}{9} [5 + 4 \cos ϕ]$
D

$\frac{I_{0}}{9} [5 + 8 \cos ϕ]$

Solution

$A s a m p l i t u d e s a r e A a n d 2 A, s o i n t e n s i t i e s w o u l d b e i n t h e r a t i o 1 : 4 L e t u s s a y I a n d 4 I I_{\max} = I_{0} = l + 4 l + 2 \sqrt{4 l^{2}} = 9 l \Rightarrow l = \frac{l_{0}}{9} I n t e n s i t y a t a n y p o i n t, l' = l + 4 l + 2 \sqrt{4 l^{2}} \cos ϕ \Rightarrow l' = 5 l + 4 l \cos ϕ = I (5 + 4 \cos ϕ) = \frac{l_{0}}{9} (5 + 4 \cos ϕ)$

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