Calculate Beam's Divergence Angle from Earth to Moon

[mars shaw]

Homework Statement

A tiny laser beam is directed from Earth to moon. If beam's diameter is 2.50 m at the moon, how small much the divergence angle be for the beam? The distance of moon from the Earth is 3.8x10^8 m

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi Mars shaw!

(try using the X² tag just above the Reply box )

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[mars shaw]

Homework Statement

A tiny laser beam is directed from Earth to moon. If beam's diameter is 2.50 m at the moon, how small much the divergence angle be for the beam? The distance of moon from the Earth is 3.8x10^8 m

Homework Equations

theta=s/r

The Attempt at a Solution

s=diameter=2.50 m
r=distance of moon from earth=3.8x10^8
theta=s/r
theta=2.50/3.8x10^8 = 6.6x10^-9 rad
I got the correct answer but I am confuse about diameter that how it can be taken as "s"?
Kindly explain.

 

[tiny-tim]

Hi Mars shaw !

Because you imagine the line from your eye to the bottom of the moon as being length r, and the diameter (s) of the moon as being at right-angles to that line, so the tangent of the angle is s/r.

(and if you're not happy about that, but you'd rather use the radius, and the line to the centre of the moon, you'll get the same result: the tangent of half the angle is (s/2)/r )