Question

g it as been suggested that solar powered space ships could get a boost from a laser either on earth or in orbit around earth. the laser would have to be very powerful to give any measurable benefit to the ship. if the laser produces a 0.18-m diameter beam of 490-nm light, what is the minimum angular spread of the beam?

Answer 1

Answer:

The minimum angular spread of the laser beam is 3.32 × $10^{-6}$ radians (or 3.32 μrad).

Explanation:

The minimum angular spread of a wave is the ratio of its narrowest diameter to its wavelength.

From Rayleigh's formula,

Angular spread = 1.22 (wavelength ÷ diameter)

                          = 1.22 (λ ÷ D)

Given that:

diameter, D = 0.18 m and wavelength, λ = 490 nm, then;

Angular spread of the laser beam = 1.22 (λ ÷ D)

                         = 1.22$(\frac{490*10^{-9} }{0.18})$

                         = 1.22× 2.7222 × $10^{-6}$

                        = 3.3211 × $10^{-6}$ rad

The minimum angular spread of the laser beam is 3.32 × $10^{-6}$ radians.