A plane wavefront of 7000 Å falls on an aperture. The area of half period zone of the diffraction pattern on screen 1 meter away from the aperture will be :

Question

Question

Answer 1

CONCEPT:

Fresnel’s Half Period Zone (HPZ):

F1 Prabhu 27.11.20 Pallavi D4

According to Fresnel’s the entire wavefront can be divided into a large number of parts of zones which are known as Fresnel’s half-period zones (HPZ’s).
The resultant effect at any point on the screen is due to the combined effect of all the secondary waves from the various zones.

EXPLANATION:

F1 Prabhu 27.11.20 Pallavi D5

\(⇒ r_n=\sqrt{ndλ}\)

Where n = number of zones, d = distance from point P to the wavefront, and λ = wavelength

An = πdλ

Calculation:

Given d = 1m, λ = 7000 Å = 7 × 10^-7 m;

Now the are of the HPZ will be

A = π × 1 × 7 × 10^-7 m²;

⇒ A = 21.99 × 10^-7 m²;

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