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Wave Optics — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsWave Optics1 Mark
Question
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.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is NOT the correct explanation of A.
  3. A is true but R is false.
  4. A is false and R is also false.
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.
✓

Answer

  1. Both A and R are true but R is NOT the correct explanation of A.

Explanation:

For case when dark fringe is observed opposite to one of the slit.

Here S1P = D and S2P $=\sqrt{\text{D}^2+\text{d}^2}=\text{D}\Big[1+\frac{\text{d}^2}{2\text{D}^2}\Big]$

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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