A spotlight sends red light (wavelength = 694.3 nm) to the moon. At the surface

Question

A spotlight sends red light (wavelength = 694.3 nm) to the moon. At the surface of the moon, which is 3.77 x 108 m away, the light strikes a reflector left there by astronauts. The reflected light returns to the earth, where it is detected. When it leaves the spotlight, the circular beam of light has a diameter of about 0.28 m, and diffraction causes the beam to spread as the light travels to the moon. In effect, the first circular dark fringe in the diffraction pattern defines the size of the central bright spot on the moon. Determine the diameter (not the radius) of the central bright spot on the moon.

I keep getting the wrong answer and I am not sure what I did wrong!

Explanation / Answer

The angle, A, between the axis and 1st dark fringe is given by sinA=1.22lambda /d (d = aperture diameter; see link).

The size of spot's radius, R, on the moon is given by tanA = R/D where D is the earth-moon distance.
R = DtanA

For small angles tanA = sinA to a good approximation
R = DtanA = DsinA = D x 1.22lambda/d = 3.77x10^8 x 1.22 x 694.3x10^-9 / 0.28 =1140m
Diameter = 2 x 1140 = 2280m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.