An object placed in front of a concave mirror at a distance of `x` cm from the pole gives a `3` times magnified real image. If it is moved to a distance of `(x+5)` cm, the magnification of the image becomes `2`. The focal length of the mirror is

Options

A. 15 cm
B. 20 cm
C. 25 cm
D. 30 cm

Answer

D

Explanation

(i) u = x, v = -3x `" " ("as m "= -3 = -(v)/(u) ) `
(ii) u = - (x + 5) , v = - 2 (x + 5) `("as m" = -2 = (-v)/(u))`
From (i) `(1)/(f) = (1)/(u) + (1)/(v) rArr (1)/(f) = - (1)/(x) - (1)/(3x) = (-3-1)/(3x) `
`rArr " " (1)/(f) = - (4)/(3x)`
`Now, (1)/(f) = (-1)/((x+ 5)) - (1)/(2(x + 5)) rArr (1)/(f) = (-2 -1)/(2(x + 5))`
`rArr - (4)/(3x) = (-3)/(2(x + 5)) rArr - 8x - 40 = - 9x`
`rArr x = 40 `cm
`(1)/(f) = (-4)/(3 xx 40) rArr f = -30 ` cm .