The limit to the eye\'s visual acuity is related to diffraction by the pupil. Ra

Question

The limit to the eye's visual acuity is related to diffraction by the pupil. Randomized Variables D = 2.8 mm dh = 1.1 m Part (a) What is the angle between two just-resolvable points of light for a 2.8 mm diameter pupil in radians, assuming an average wavelength of 550 nm? Part (b) Take your result to be the practical limit for the eye. What is the greatest possible distance in km a car can be from you if you can resolve its two headlights, given they are 1.1 m apart? Part (c) What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye in mm?

Explanation / Answer

The Rayleigh criterion stated in the equation =1.22/D gives the smallest possible angle between point sources, or the best obtainable resolution. Once this angle is found, the distance between stars can be calculated, since we are given how far away they are.

The Rayleigh criterion for the minimum resolvable angle is

=1.22/D.

Entering known values gives

=1.22*550×109m/ 2.8x10-3 m= 2.39×104 rad............Ans.

(b) we know that distance s = r*

s = 1.1 * 2.39×104 = 2.63×104 m or 2.63×107 km

(c)   s = 0.8 * 2.39×104 = 1.912×104 m

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