This question is about resolution (a) State the ayleigh criterion for the images

Question

This question is about resolution (a) State the ayleigh criterion for the images of two point sources to be just resolved. A man is walking along a straight path at night towards two light sources as shown below. light sourcesO path man not drawn to scale When the man is 150 m from the sources, the images of the two sources are just resolved by his eye. The wavelength of the light from each source is 590 nm and the diameter of the aperture of his eye is 5.0 mm (b) Estimate the distance between the two sources

Explanation / Answer

part a:

Rayleigh criterion is related to angular resolution or spatial resolution .

angular resolution is defined as the ability of any image forming device to distinguish between two different objects.

for sources of equal strength and considering diffraction through circular aperture,

criterion is given as:

theta=1.22*lambda/D

where theta=angular resolution in radian

lambda=wavelength of light

D=diameter of the lens’ aperture

part b:

let distance between two sources be d.

considering d << L where L=distance of the lens from the objects,

angle theta=arctan(d/L)=d/L

given L=150 m

lambda=590 nm=590*10^(-9) m

D=5 mm=0.005 m

hence using rayleigh criterion,

d/150=1.22*590*10^(-9)/0.005

==>d=150*1.22*590*10^(-9)/0.005

==>d=0.021594 m

=2.16 cm

hence distance between two objects is 2.16 cm

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