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

given

Diameter of the mirror is 2.4 m, and wavelength of the light is lambda = 670 nm = 670 *10^-9 m

   X = 30000 ly
we know that the resolving power of a telescope is R.P = 1.22*lambda/ D

   R.P = 1.22*670*10^-9 / 2.4 = 3.40 *10^-7

PART A)
   which is equal to X/ 30000 ly

   ==> y = 3.40*10^-7*30000*3*10^8*365*24*60*60*10^-3 km
   y = 9.65*110 km
PART B)

distance between jupiter and sun is = 778.5 million km

   now y = 9.65*10^10/778.5*10^6
   = 123.96 times the distance between jupiter and sun

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