First slide

Diffraction of light-Wave Optics

Question

In a Fresnel’s diffraction arrangement, the screen is at a distance of 2 meter from a circular aperture. It is found that for light of wavelengths $λ_{1}$ and $λ_{2},$ the radius of $4 t h$ zone for $λ_{1}$ coincides with the radius of $5 t h$ zone for $λ_{2} .$ Then the ratio $λ_{1} : λ_{2}$ is

Moderate

A

$\sqrt{4 / 5}$
B

$\sqrt{5 / 4}$
C

$5 / 4$
D

$4 / 5$

Solution

$I t i s g i v e n t h a t r_{4} = \sqrt{4 b λ_{1}} a n d r_{5} = \sqrt{5 b λ_{2}} a r e e q u a l . T h e r e f o r e \sqrt{4 b λ_{1}} = \sqrt{5 b λ_{2}} o r 4 b λ_{1} = 5 b λ_{2} o r \frac{λ_{1}}{λ_{2}} = \frac{5}{4} .$

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