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Intensity Explanation in YDSE

In a Young's ...

Question

In a Young's Double Slit experiment, films of thickness $t_{A}$ and $t_{B}$ and refractive indices $μ_{A}$ and $μ_{B}$ are placed in front of slits A and B respectively. If $μ_{A} t_{A} = μ_{B} t_{B}$ , then the central maxima may

A

not shift

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B

shift forwards A

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C

shift towards B

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D

None of these

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Solution

The correct options are
A not shift
B shift forwards A
C shift towards B
The path difference
$Δ x = (μ_{A} - 1) t_{A} - (μ_{B} - 1) t_{B}$
$\Rightarrow Δ x = μ_{A} t_{A} - t_{A} - μ_{B} t_{B} + t_{B}$
$\Rightarrow Δ x = t_{B} - t_{A}$
if $t_{B} = t_{A} \Rightarrow Δ x = 0$
$\Rightarrow$ no shift
if $t_{B} > t_{A} o r t_{B} < t_{A}$
$Δ x \neq 0$
$\Rightarrow$ central maxima may shift towards A or B.

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