A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm from each other. A point object placed 40 cm in front of the convex lens. Find the position of the image formed by this combination.

For convex lens,Focal length,f=+20 cmObject distance,u=-40 cmUsing lens formula, we have1f=1v-1u120=1v-(-40) ⇒1v=120-140=240⇒v=+40 cmNow, for convex mirror, we haveFocal length,f=R2=202=+10 cmObject distance,u=+(40-15) cm=+25 cmUsing mirror formula, we have1f=1v+1u110=1v+125⇒1v=110-125=550=350⇒v=+503 cm∴The final image is formed at a distance of503 cmfrom the convex mirror or at a distance of(503 +15)cm=953cmfrom the convex lens.The final image is a virtual image.