A convex lens of focal length 20cm is places coaxially with a convex mirror of radius of curvature 20cm. The two are kept at 15 cm from each other. A point object lies 60cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

Explanation

For the convex lens
`u = - 60cm, f = + 20cm`
`(1)/( v) - ( 1)/( u ) = ( 1)/( f)`
`( 1)/( v) - ( 1)/( - 60) = (1)/( 20)`
` ( 1)/(v) = ( 1)/( 20) - ( 1)/( 60) = ( 2)/( 60) = ( 1)/( 30)`
`v = 30 cm`
For the convex mirror
`u = + ( 30-15)cm = 15cm, f = + ( 20)/( 2) cm = 10cm `
`(1)/( v ) + ( 1)/( u ) = ( 1)/( f)`
` ( 1)/( V ) + ( 1)/.( 15) = ( 1)/( 10) `
`(1)/(v) = ( 1)/( 10) - (1)/( 15) = ( 3-2)/( 30) = ( 1)/( 30)`
`v = 30cm`
Final image is formed at the distance of 30cm from the convex mirror ( or 45 cm from the convex lens ) to the right of the convex mirror.
The final image formed is a virtual image.