Question

The Hubble Space Telescope (still operational) has a mirror with a diameter of 2.4 m. What is the maximum resolution of Hubble when observing Mars at closest approach (typically 7.5 x 1010 m away)? Since Mars is mostly red, assume the light is reddish, with a wavelength of 630 nm. Could Hubble resolve the Endeavor crater (diameter 22 km) on Mars? 1. 2. Calculate the angle of incidence at which light reflecting off of crown glass (with an index of refraction of n1.86) have the reflected light completely polarized (Brewster's angle). Then calculate the angle of refraction for this angle of incidence, and verify that the reflected and refracted beams are perpendicular

Answer 1

1] Use Rayleigh's diffraction limit criteria,

$d\frac{x}{D}=1.22\lambda$

here, d = 2.4 m, D = 7.5 x 10¹⁰ m and wavelength = 630 nm

=> $2.4\frac{x}{7.5\times 10^{10}}=1.22(630\times 10^{-9})$

=> x = 24018.75 m = 24.018 km

this is the smallest detail captured by the telescope and since this is greater than 22km, the telescope will not be able to resolve the Endeavor crater on Mars.