Question

A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the Moon.

(a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam?
(b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the Moon, assuming a lunar distance of 3.84×10⁸ m ?

Answer 1

The minimum angular spread of the laser beam is 2.63 × 10^-6 radians. The size of the spot this beam would make on the Moon is 1.01x10^3 m.

Step-by-step explanation:

The minimum angular spread of a laser beam can be determined using the equation θ = 1.22 * λ / D, where θ is the angular spread, λ is the wavelength of the light, and D is the diameter of the beam. In this case, the Mount Wilson telescope produces a 2.54-m-diameter beam of 633-nm light.

Plugging these values into the equation gives θ = 1.22 * (633 nm / 1000000000 m/nm) / 2.54 m = 2.63 × 10^-6 radians.

The size of the spot this beam would make on the Moon can be calculated using the formula: Size = θ * distance, where distance is the lunar distance of 3.84 × 10^8 m. Substituting the value of θ into the formula gives Size = 2.63 × 10^-6 radians * 3.84 × 10^8 m = 1.01x10^3 m.