Wave Optics - Result Question 13
13. In a double slit experiment, the two slits are 1 $mm$ apart and the screen is placed $1 m$ away. A monochromatic light wavelength $500 nm$ is used.
What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?
(a) $0.1 mm$
(b) $0.5 mm$
(c) $0.02 mm$
(d) $0.2 mm$
[2015]
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Answer:
Correct Answer: 13. (d)
Solution:
- (d) Here, distance between two slits, $d=1 mm=10^{-3} m$ distance of screen from slits, $D=1 m$ wavelength of monochromatic light used, $\lambda=500 nm=500 \times 10^{-9} m$ width of each slit $a=$ ?
Width of central maxima in single slit pattern $=\frac{2 \lambda D}{a}$
Fringe width in double slit experiment $\beta=\frac{\lambda D}{d}$
So, required condition $\frac{10 \lambda D}{d}=\frac{2 \lambda D}{a}$
$\Rightarrow \quad a=\frac{d}{5 D}=\frac{1}{5} \times 10^{-3} m=0.2 mm$
