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The box of a pin hole camera, of length L, has hole of radius a. it is assumed that when the hole is illuminated by a parallel beam of light of wavelength  the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say bmin) when : a=_____ ?; b(min)=_____? Please explain the method

The box of a pin hole camera, of length L, has hole of radius a. it is assumed that when the hole is illuminated by a parallel beam of light of wavelength  the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say bmin) when :  
a=_____ ?; b(min)=_____?
 
Please explain the method

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
spot size (diameter) b = 2 (\lambdaL / 2a) + 2a
a^2 + \lambda l – ab = 0
For real roots
b^2 – 4\lambdaL >= 0
b min = \sqrt4\lambdaL
by eqn (i)
a = \sqrt\lambdaL

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