Q45E - University Physics with Modern Physics

Question

You are asked to design a space telescope for earth orbit. When Jupiter is $\mathbf{5}\mathbf{.}\mathbf{93}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{km}$away (its closest approach to the earth), the telescope is to resolve, by Rayleigh’s criterion, features on Jupiter that are 250 km apart. What minimum-diameter mirror is required? Assume a wavelength of 500 nm.

Step-by-Step Solution

Answer

The minimum diameter of the mirror is 1.45m.

Step 1: Rayleigh’s Criterion

According to the Rayleigh criterion for the diffraction limit to resolution, two images are only resolvable when the center of one's diffraction pattern is directly over the first minimum of the other's diffraction pattern.

Step 2: Minimum-diameter mirror

Putting the values;

Hence, the minimum diameter of the mirror is 1.45m.