A lens that is \"optically perfect\" is still limited by diffraction effects. Su

Question

A lens that is "optically perfect" is still limited by diffraction effects. Suppose a lens has a diameter of 120 mm and a focal length of 680 mm.

Part A

Find the angular width (that is, the angle from the bottom to the top) of the central maximum in the diffraction pattern formed by this lens when illuminated with 510 nm light. Answer in radians in two significant figures.

Part B

What is the linear width (diameter) of the central maximum at the focal distance of the lens? Answer in radians in two significant figures.

Explanation / Answer

Given,

Diameter, D = 120 mm

Focal length, f = 680 mm

Wavelength, lambda = 510 nm

A)

Angular radius, theta = 1.22 lambda /D

Theta = (1.22 x 510 x 10^-9)/0.12 = 5.185 x 10^-6 rad

Angular diameter = 2 x theta = 1.04 x 10^-5 rad

B)

Radius of central maximum, R = 1.22 f lambda /D

Diameter, d = 2R

d = (2 x 1.22 x 0.68 x 510 x 10^-9)/0.12 = 7.05 x 10^-6 m

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