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Wave Optics — Physics STD 12 Science — Question

Gujarat 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 $A.$
  • ✓
    Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
  • C
    $A$ is true but $R$ is false.
  • D
    $A$ is false and $R$ is also false.
✓

Answer

Correct option: B.
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
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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