p37_026.pdf

26. We denote the Earth-Moon separation as L . The energy of the beam of light which is projected onto the

moon is concentrated in a circular spot of diameter d 1 ,where d 1 /L =2 θ R =2(1 . 22 λ/d 0 ), with d 0 the

diameter of the mirror on Earth. The fraction of energy picked up by the reﬂector of diameter d 2 on the

Moon is then η =( d 2 /d 1 ) 2 . This reﬂected light, upon reaching the Earth, has a circular cross section

of diameter d 3 satisfying d 3 /L =2 θ R =2(1 . 22 λ/d 2 ). The fraction of the reﬂected energy that is picked

up by the telescope is then η =( d 0 /d 3 ) 2 . Consequently, the fraction of the original energy picked up

by the detector is

η = η η = d 0

d 3

2 d 2

d 1

= d 0 d 2

(2 . 44 λd em /d 0 )(2 . 44 λd em /d 2 )

= d 0 d 2

2 . 44 λd em

(2 . 6m)(0 . 10 m)

≈

10 − 13 .

2 . 44(0 . 69

10 − 6 m)(3 . 82

10 8 m)