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 :

  1. 28 × 10-7 m2
  2. 44 × 10-7 m2
  3. 22 × 10-7 m2
  4. 14 x 10-7 m2

Answer (Detailed Solution Below)

Option 3 : 22 × 10-7 m2
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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

  • The radius of half period zone is:

\(⇒ r_n=\sqrt{ndλ}\)

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

  • The Area of the nth HPZ is given by 

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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