Numerical Questions and answers

                 Physics Numericals:

Question 1. Find out the resolving power of a human eye for yellow light of wavelength 600 nm assuming an average pupil's size is 5 mm.

Answer:  The resolving power of the human eye, also known as the angular resolution, refers to the smallest angle between two point sources of light that can be distinguished by the eye. It is determined by several factors, including the wavelength of the light, the size of the pupil, and the quality of the optics of the eye.

The minimum angle of resolution (MAR) can be calculated using the Rayleigh criterion, which states that two point sources can be distinguished if the center of one diffraction pattern falls on the first minimum of the other diffraction pattern.

The Rayleigh criterion is given by:

θ = 1.22 λ/D

where θ is the angular resolution in radians, λ is the wavelength of light in meters, and D is the diameter of the pupil in meters.

Converting the values given in the question to SI units, we have:

λ = 600 nm = 6.00 × 10^-7 m

D = 5 mm = 5.00 × 10^-3 m

Plugging these values into the formula gives:

θ = 1.22 × 6.00 × 10^-7 / 5.00 × 10^-3 = 1.464 × 10^-4 radians

Converting this to arcminutes (1 degree = 60 arcminutes), we get:

θ = 1.464 × 10^-4 × 60 = 8.784 × 10^-3 arcminutes

Therefore, the resolving power of the human eye for yellow light of wavelength 600 nm with an average pupil size of 5 mm is approximately 8.784 × 10^-3 arcminutes.