Question

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.

Answer 1

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

Step-by-step 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 (
`B_(30)`) of 30 m telescope would be proportional to
`30^2`

Brightness of 10 m (
`B_(10)`} telescope would be proportional to
`10^2`

Thus, the ration of the two would be

`(B_(30))/(B_(10)) = (30^2)/(10^2) \\(B_(30))/(B_(10)) = (9)/(1) \\B_(30) = 9 * B_(10)`

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