A convex lens of focal length `20 cm` and a convex mirror of focal length `10 cm` are placed co-axially `50 cm` apart from each other. An incident beam parallel to its principal axis is incideent on the convex lens. Locate the position of final image formed due to the combination.

Explanation

We have `u=oo,f_(1)=20cm,f_(m)=10cm,d=50cm`
For convex lens :
`(1)/(v)-(1)/(u)=(1)/(f)or(1)/(u)=(1)/(f)+(1)/(u)or`
`therefore" "(1)/(u)=(1)/(20)+(1)/(oo)=(1)/(20)thereforev=210cm.`
Fro concave mirror :
`u=50-20=-30cm,f=-10cm `
`(1)/(v)+(1)/(u)=(1)/(f)or(1)/(v)=(1)/(f)-(1)/(u)`
`therefore " " (1)/(v)=(1)/(-10)-(1)/(-30)=(-3+1)/(30)=(-20)/(30)=-(1)/(5)`
`therefore " " v=-15cm.`