First slide

Coherent sources and their importance in interference

Question

To make the central fringe at the center O. A mica sheet of refractive index 1.5 is introduced. Choose the correct statements(s)

Moderate

A

$The thickness of sheet is 2 (\sqrt{2} - 1) d in front of S_{1}$
B

$The thickness of sheet is 2 (\sqrt{2} - 1) d in front of S_{2}$
C

$The thickness of sheet is 2 \sqrt{2} d in front of S_{1}$
D

$The thickness of sheet is (2 \sqrt{2} - 1) d in front of S_{1}$

Solution

To make path difference 0 at O.
Mica sheet has to be introduce in front of $S_{1}$
Geometrical path difference before entering slits should be balanced by optical path difference due to mica sheet.
Before entering slits $∆ x_{G e o m} = S S_{2} - S S_{1} = \sqrt{2} d - d = (\sqrt{2} - 1) d$
After passing through slits $∆ x_{o p t i c a l} = S_{1} O - S_{2} O = (μ - 1) t$
$\begin{array}{l} (\sqrt{2} - 1) d = (μ - 1) t \\ \Rightarrow t = \frac{(\sqrt{2} - 1) d}{(μ - 1)} \\ \Rightarrow t = 2 (\sqrt{2} - 1) d \end{array}$

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