Previous Year NEET Question- Wave Optics L-5

Question: A linear aperture whose width is $0.02 \mathrm{~cm}$ is placed immediately in front of a lens of focal length $60 \mathrm{~cm}$. The aperture is illuminated normally by a parallel beam of wavelength $5 \times 10^{-5} \mathrm{~cm}$. The distance of the first dark band of the diffraction pattern from the centre of the screen is#

A) $0.10 \mathrm{~cm}$

B) $0.25 \mathrm{~cm}$

C) $0.20 \mathrm{~cm}$

D) $0.15 \mathrm{~cm}$

Answer: $0.15 \mathrm{~cm}$#

Sol:#

$$ \begin{aligned} & \text { Here, } a=0.02 \mathrm{~cm}=2 \times 10^{-4} \mathrm{~m} \ & \lambda=5 \times 10^{-5} \mathrm{~cm}=5 \times 10^{-7} \mathrm{~m} \ & D=60 \mathrm{~cm}=0.6 \mathrm{~m} \end{aligned} $$

Position of first minima on the diffraction pattern, $$ y=\frac{D \lambda}{a}=\frac{0.6 \times 5 \times 10^{-7}}{2 \times 10^{-4}}=15 \times 10^{-4} \mathrm{~m}=0.15 \mathrm{~cm} $$