A concave mirror of focal length 20 cm and a convex lens of focal length 10 cm are kept with their optic axes parallel but separated by 0.5 mm as shown in the figure. The distance between the the lens and mirror in 10 cm. An object of height 3 mm is placed on the optic axis of lens at a distance between the lens and mirror is 10 cm. An object of height 3 mm is placed on the optic axis of lens at a distance 15 cm from the lens. Find the length of the image formed the mirror in mm.

Answer

`3`

Explanation

For image formed by the lens
`1/(v_(1))-1/(-15)=1/(+10)`
`impliesv_(1)=+30cm`
i.w. 20 cm behind mirror
For mirror
`1/(v_(2))+1/20=1/(-20)`
`impliesv_(2)=-10cm`
overall magnification=
`(30/(-15))xx(10/20)=-1`
Length of image `=1xx3=3mm`