Question

The ratios of object distance to Image distances are u1:v1= 2:3 for a concave mirror and u2:v2 = 7:4 for a convex mirror when an object is placed exactly at same distance for both mirror individually. Find the ratio of the focal lengths of the mirrors?

Answer 1

Answer:

Let the object be at a distance x from the plane mirror.

The distance of object from concave mirror=u=50-x

For the plane mirror, object and image distances are equal.

A′=AM=x

⇒OA′=OM+A′M=50+x

For the concave mirror,v=50+x

Using u=−(50−x),v=−(50+x),f=−16cm

150−x+150+x=116

100502−x2=116⇒x=30cm

The object must be placed at a distance of 30 cm from the plane mirror.

The ratio of image sizes

=A′B′A′B''=ABA′B''=uv=50+x50−x=14

The real image formed by the concave mirror is four times the size of virtual image formed by the plane mirror.

Explanation:

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