Question

A laser beam, shining from the earth's surface, is directed at the moon whose distance from the earth on this day is 370,000 km. If the beam diverges at an angle of only 1.65 x 10-5 rad, what diameter circle will it make on the moon

Answer 1

d = 6105 m

Step-by-step explanation:

For this exercise we must use trigonometry to find the diameter of the has. The most common definition in optics of the angle of divergence is measured between the two ends of the beam, therefore to use this angle in trigonometry where the angle is measured with respect to the normal we must take half of this angle

θ = 1.65 10⁻⁵ / 2 = 0.825 10⁻⁵ rad

let's use the tangent

tan θ = y / L

y = L tan θ

y = 370000 103 tan (0.825 10⁻⁵)

let's be careful since the angles are in radians

y = 3025.5 m

This is the distance from the normal that corresponds to the radius of the circle, the diameter is twice the radius

d = 2 y

d = 2 3025.5

d = 6105 m