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 apart 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

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Applying lens formula for convex lens,

1v-1u=1f

⇒ 1v-1-60=120

⇒ v=30cm

Image (I1) formed by the convex lens acts as an object for the convex mirror.

Since the mirror and lens are separated by 15 cm, the distance between I1 and mirror is 15 cm. Therefore,  object from mirror becomes u'=15cm

Applying mirror formula for convex mirror,

1v'+1u'=1f'

⇒ 1v'+115=2R   (focal length of mirror, f' =R2)

⇒1v'+115=110

⇒ v'=30cm

Hence, the image is formed 30 cm right of the convex mirror

convex lens

Nature of the image is virtual.

Position of the image is 30 cm right of the convex mirror.

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