The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope

Question

The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 670 nm .

Part A

What's the distance (in km) between two stars that are marginally resolved? The resolution of a reflecting telescope is calculated exactly the same as for a refracting telescope.

Express your answer using two significant figures.

Part B

For comparison, what is this distance as a multiple of the distance of Jupiter from the sun?

Express your answer using two significant figures.

Explanation / Answer

a)

Considering diffraction through a circular aperture

= 1.220 /D

where

is the angular resolution (radians),

is the wavelength of light,

and D is the diameter of the lens' aperture

and and D are expressed in the same units (centimeters, meters).

= 3.41*10^-7

by using paraxial approximation sin =tan =
=x/(30000x9.4605284 × 10^12 kilometers)

x =9.678*10^10 km

b). dividing x =9.678*10^10 km by the average distance of jupiter to the sun(778,412,010)

= 124 Ans

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