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:

  1. (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 $\frac{10 \lambda D}{d}=\frac{2 \lambda D}{a}$

$\Rightarrow \quad a=\frac{d}{5 D}=\frac{1}{5} \times 10^{-3} m=0.2 mm$