Wave Optics - Result Question 11
11. Young’s double slit experment is first performed in air and then in a medium other than air. It is found that $8^{\text{th }}$ bright fringe in the medium lies where $5^{\text{th }}$ dark fringe lies in air. The refractive index of the medium is nearly
(a) 1.59
(b) 1.69
(c) 1.78
(d) 1.25
[2017]
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Answer:
Correct Answer: 11. (c)
Solution:
- (c) According to question $8^{\text{th }}$ bright fringe in medium $=5$ th dark fring in air $Y _{8 \text{ th bright }}=8 \frac{\lambda D}{\mu d}$
$Y _{5 \text{ th dark }}=(2 \times 5-1) \frac{\lambda D}{2 d}=\frac{9}{2} \frac{\lambda D}{d}$
$\Rightarrow \quad \frac{9}{2} \frac{\lambda D}{d}=8 \frac{\lambda D}{\mu d}$
or, refractive index $\mu=\frac{16}{9}=1.78$
In YDSE for constructive or bright fringes. $Y_n=\frac{n D \lambda}{d}$ for $n$th bright fringe and for destructive or dark fringes. $y_n=(2 n-1) \frac{D \lambda}{2 d}$ for $n$th dark fringe.
