If the tube length of astronomical telescope is 105 cm and magnifying power is 20 for normal setting, then the focal length of the objective is .......... cm.

Options

A. 10
B. 20
C. 25
D. 100

Answer

A, D

Explanation

For astronomical telescope,
Tube length `L ge f_0+f_e` …....(1)
Magnification m=`(f_0)/(f_e)impliesf_e=(f_0)/(m)`…........(2)
From eqn.(1) and (2),
`L ge f_0+(f_0)/(m),L=105,m=20,`
`105 ge f_0(1+(1)/(20))ge f_0((21)/(20))`
`f_0 le (105xx20)/(20) le 100`
`implies f_0=100`