A cube of side 2m is placed in front of a concave mirror of focal l ength 1m with its face A at a distance of 3m and face B at a distance of 5m form the mirror. The distance between the images of faces A and B and heights of images of A and B are , repectively,

Options

A. 1 m, 0.5 m, 0.25 m
B. 0.5 m, 1 m, 0.25 m
C. 0.5 m, 0.25 m, 1m
D. 0.25 m, 1m, 0.5 m

Answer

D

Explanation

For surface P-
`u_(1) = -3, f = -1 `m
`(1)/(v_(1)) = (1)/(f) - (1)/(u) = - 1 + (1)/(3) = -(2)/(3)`
`rArr " "v_(1) = -(3)/(2) m - 1.5 ` m
For surface Q-
`u_(2) = -5 m, f = - 1 ` m
`(1)/(v_(2)) = - 1 + (1)/(5) = (-4)/(5)`
`rArr v_(2) = (-5)/(4) = -1.25` cm
`therefore " " v_(1) -v_(2) = -1.25 - (-1.5) = 0.25` m
Magnification of P `= (v_(1))/(u_(1)) = (-3//2)/(-3) = (1)/(2)`
Height of image P = `(1)/(2) xx 2 = 1 `m
Magnification of Q = `(v_(2))/(u_(2)) = (-5//4)/(-5) = (1)/(4)`
Height of image Q = `(1)/(4) xx 2 = 0.5 `m.