7. Telescope efficiency depends on the area of the primary mirror, while angular resolution scales as 1/D, where D is the diameter of the telescope. State which is true concerning the objects observed with a 30m telescope, versus a 10m telescope. A) The 30 m telescope can observe objects 30 times fainter, and with 3 times the resolution of the 10 m telescope. B) The 30 m telescope can observe objects with 1/9 the angular diameter, and 9 times fainter than, the 10 m telescope. C) The 30 m telescope can observe objects 9 times fainter, and with 3 times smaller angular size, than the 10 m telescope. D) The 30 m telescope can observe objects 3 times fainter, and with 3 times smaller angular size, compared to the 10 m telescope.

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podgorica podgorica · Answer 1 · 2021-04-29T19:20:30+02:00

Answer:

Option C, The 30 m telescope can observe objects 9 times fainter, and with 3 times smaller angular size, than the 10 m telescope.

Explanation:

As we know,

The surface brightness of the object viewed through telescope is proportional to the square of the diameter of the lens

Thus, Brightness ([tex]B_{30}[/tex]) of 30 m telescope would be proportional to [tex]30^2[/tex]

Brightness of 10 m ([tex]B_{10}[/tex]} telescope would be proportional to [tex]10^2[/tex]

Thus, the ration of the two would be

[tex]\frac{B_{30}}{B_{10}} = \frac{30^2}{10^2} \\\frac{B_{30}}{B_{10}} = \frac{9}{1} \\B_{30} = 9 * B_{10}[/tex]

Thus, brightness of 30 m telescope would be able to view 9 times fainter object as compared to the 10 m telescope.

Also , 30 m telescope would be able to view 3 times smaller angular sized object as compared to the 10 m telescope

Hence, option C is correct