Question

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. 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.

Answer 1

Image is formed 30 cm right of the convex mirror and the image is virtual.

Explanation:

Lens formula for convex lens:

1/v - 1/u = 1/f

1/v - 1/-60 = 1/20

v = 30 cm

• 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, distance between I1  and mirror is 15 cm.

i.e. u = 15

For convex mirror:

f = R/2 = 10 cm

From mirror equation:

1/v2 - 1/u2 = 1/f2

1/v2 + 1/15 = 1/10

V2 = 30 cm

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

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A concave mirror of focal length 15 cm forms an image of an object kept at a distance of 10 cm from the mirror.Find the position, nature and size of the image formed by it by drawing a ray diagram. ?

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