Light of lambda = 500 nm enters the pupil of a human eye. Assuming the resolutio

Question

Light of lambda = 500 nm enters the pupil of a human eye. Assuming the resolution of the human eye is limited only by diffraction and that the average diameter of the pupil is 2.0 mm, what does the Raleigh criterion give as the limiting angle of resolution of the eye (visual acuity) (b) What is the resolution of 200 inch Mount Palomar reflector for this wavelength? (c) the radio telescope at Arecibo, Puerto Rico, has a diameter of 312 m and is designed to detect radio waves of lambda = 0.75 m. What is its resolution? How does it compare to the human eye?

Explanation / Answer

(a) As per diffraction limited resolution criteria, resolution is given by
Resolution, R=1.22(wavelenght of light)/D where D is size of aperture
So putting all these values,R=1.22*500*10^{-9}/2*10^{-3}
R=305*10^{-6}

(b) Since, One inch=2.54cm
R=1.22*500*10^{-9}/{200*2.54*10^{-2}=1.20*10-7

(c) For radio wave detection, Resolution, R=1.22*0.75/312=2.93*10-3, which is very less resolution as compared to human eye, 1000 times less resolution.

So, human eye has a better resolving power.

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