A convex lens of focal length 30 cm is placed coaxially with a convex mirror of radius of curvature 20 cm

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ray-optics

#1

A convex lens of focal length 30 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 lies 60 cm 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.


#2

The ray diagram showing the image formation is given below:

O is at 2f of lens, so it will form image at 2f on other side, i.e. 60 cm from lens. Hence, position of object from mirror is at (60 -15) cm = 45 cm behind the mirror.

For mirror,

f = +10 cm,
u = +45 cm,
v = ?

As 1/v + 1/u = 1/f
===> 1/v + 1/45 = 1/10

v = +90/7 cm