Question

There is a convex mirror of focal length of 30 cm. A point object O is placed in front of the convex mirror at a distance of 15 cm. A plane mirror is kept at some distance from the convex mirror. If the distance between the two images (one formed by direct reflection at the plane mirror and the other formed by a reflection at convex mirror followed by a reflection at the plane mirror) of the object formed in the plane mirror is 25 cm, find the separation between the plane mirror and the convex mirror

Answer 1

Answers

We are given

f = -15 cm( ?????? I don't think its correct , convex mirror has a negative focal length)

u = -30 cm

and the image distance will be calculated using

1/f = 1/v + 1/u

or

1/v = 1/f + 1/u

= 1/-15 - 1/30

or

1/v = (-2 - 1)/30 = -3/30

thus, we have

v = -10 cm

now, the image formed would be 30cm behind the convex so the total distance between the object and image will be

= 30cm + 10cm = 40cm.

The plane mirror needs to placed at a distance of 20cm from the object in order for the image to coincide as it will form 20 cm behind it. The total distance would thus have to be 40cm.