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Wave Optics — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsWave Optics1 Mark
MCQ
For question two statements are given-one labelled Assertion $(A)$ and the other labelled Reason $(R)$. Select the correct answer to these questions from the codes $(a), (b), (c)$ and $(d)$ as given below.
Assertion $(A)$: In Young's double slit experiment the two slits are at distance $d$ apart. Interference pattern is observed on a screen at distance $D$ from the slits. At a point on the screen when it is directly opposite to one of the slits, a dark fringe is observed. Then the wavelength of wave is proportional to square of distance of two slits.
Reason $(R)$ : For a dark fringe intensity is zero.
  • A
    Both $A $ and $R$ are true and $R$ is the correct explanation of $A$.
  • B
    Both $A$ and $R$ are true but $R $ is $\text{NOT}$ the correct explanation of $A$.
  • C
    $A$ is true but $R$ is false.
  • ✓
    $A$ is false and $R$ is also false.
✓

Answer

Correct option: D.
$A$ is false and $R$ is also false.
For case when dark fringe is observed opposite to one of the slit.
Here $S_1P = D$ and $S_2P =\sqrt{\text{D}^2+\text{d}^2}=\text{D}\Big[1+\frac{\text{d}^2}{2\text{D}^2}\Big]$
Path difference $=\text{S}_2\text{P}-\text{S}_1\text{P}=\frac{\text{d}^2}{2\text{D}}=\frac{\lambda}{2}$ or, $\lambda=\frac{\text{d}^2}{\text{D}}$.

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