A convex lens of focal length 20cm is placed coaxilly with a convex mirror of radius of curvature 20 cm. The two are kept 15 cm apart. A point object is placed 40 cm in front of the convex lens. Find the position of the image formed by this combination. Draw the ray diagram showing the image formation.

Explanation

First refraction from lens
`u=-40`
`(1)/(v)-(1)/(u)=(1)/(f)`
Then `v=+40 cm`.
`I_(1)` will be set as object for convex mirror
Then `v=+25 f=10 cm v=?`
`(1)/(v)+(1)/(25)=(1)/(10)`
`v=(50)/(3)`
Then refraction by lens :
`u=-(15+(50)/(3))=-(95)/(3) cm`
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)+(3)/(95)=(1)/(20)`
`v=(20xx95)/(35)`
`v=54/28 cm`
Final image will be left of lens at `54.28 cm` .