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

Answer

d.

Explanation

For A:
`u=-3m, v_(1)=?, f=-1m`
`(1)/(u_(1))=(1)/(f)-(1)/(u)=(1)/(-1)-(1)/(-3)=(1)/(3)-1=-(2)/(3)`
or `v_(1)=-(3)/(2)`
For B:
`(1)/(v_(2))=(1)/(-1)-1/(-5)=-(4)/(5)`
or `1/v_(2)=1/5-1=-(4)/(5)` or `v_(2)=-5/4 m`
Now, `v_(1)-v_(2)=(3)/(2)-(-(5)/(4))`
`=-(3)/(2)+(5)/(4)=-(1)/(4)m =-0.25m`
Again, `(l_(1))/(O)=-(v_(1))/(u)`
or `l_(1)=-(v_(1))/(u)O=-((-3)/(2))((-1)/(3))=-1m`
Again, `(l_(2))/(O)=-(v_(2))/(u)`
or `l_(2)=-(-(5)/(4))((1)/(-5))2=-0.5m`