Question

An amateur astronomer looks at the moon through a telescope with a 15-cm-diameter objective. What is the minimum separation between two objects on the moon that she can resolve with this telescope? Assume her eye is most sensitive to light with a wavelength of 550 nm.
A. 120 m B. 1.7 km C. 26 km D. 520 km

Answer 1

Answer:

  y = 128.0 km

Explanation:

The minimum separation of two objects is determined by Rayleygh's diffraction criterion, which establishes that two bodies are solved if the first minino of diffraction of one coincides with the central maximum of the second, with this criterion the diffraction equation remains

                       

the diffraction equation for the first minimum is

                       a sin θ = λ

In the case of circular openings, the equation must be solved in polar coordinates, leaving the expression, we use the approximation that the sine of tea is very small.

                    θ =  1.22 λ / d

                   d = 15 cm

to find the distance we can use trigonometry

             tan θ = y / L

             tan θ = sin θ / cos θ = θ

substituting

              y / L = λ / d

              y = L λ /d

let's calculate

              y = 384 10⁸ 500 10⁻⁹ / 0.15

              y = 1.28 10⁵ m

Let's reduce to km

             y = 1.28 10⁵ m (1km / 10³ m)

             y = 128.0 km

the correct answer is 120 km away