A diffraction-limited laser of length and aperture diameter d generates light of wavelength $\lambda$.If the beam is directed at the surface of the Moon a distance D away, the radius of the illuminated area on the moon is approximately:
A)dD/
B)dD/$\lambda$
C)D$\lambda$ /
D)D$\lambda$/d
E)$\lambda$/ d

Question

A diffraction-limited laser of length  and aperture diameter d generates light of wavelength $\lambda$.If the beam is directed at the surface of the Moon a distance D away, the radius of the illuminated area on the moon is approximately:
A)dD/ 
B)dD/$\lambda$ 
C)D$\lambda$ / 
D)D$\lambda$/d 
E)$\lambda$/ d

Quizplus · Accepted Answer

The radius of the illuminated area on the Moon can be estimated using the formula for the diffraction limit of a circular aperture, which is approximately $ \theta = 1.22 \frac{\lambda}{d} $, where $ \theta $ is the angular radius of the diffraction pattern, $ \lambda $ is the wavelength of the light, and $ d $ is the diameter of the aperture. The linear radius $ R $ of the illuminated area at a distance $ D $ can be found by $ R = D \theta \approx D \cdot 1.22 \frac{\lambda}{d} $. The factor 1.22 is often omitted for rough estimates, leading to $ R \approx \frac{D\lambda}{d} $, which corresponds to choice D.

A Diffraction-Limited Laser of Length and Aperture Diameter D λ\lambdaλ

A Diffraction-Limited Laser of Length and Aperture Diameter D $\lambda$