Question

Radius of $1^{\text{st}}$ dark ring of Fraunhofer diffraction pattern produced by a circular aperture of radius $0.02\text{cm}$ at focal plane of convex lens of focal length $20\text{cm}$ and by light of wavelength $\lambda =600\text{nm}$ is

• A. 0.7 mm
• B. 0.36 mm
• C. 1.3 mm
• D. 2 cm

Answer 1

The correct option is B 0.36 mm

$\sin \theta =\theta =\frac{1.22\lambda }{D}$ and $\theta =\frac{R_1}{f}$

So, $R_1=\frac{1.22\lambda f}{D}=\frac{1.22\times 600\times {10}^{-9}\times 20\times {10}^{-2}}{2\times 0.02\times {10}^{-2}}$

$\Rightarrow R_1=0.37\text{mm}$