Question

A convex mirror has a focal length of
18 cm. The image of an object kept
in front of the mirror is half the height
of the object. What is the distance of
the object from the mirror?​

Answer 1

We have f=18cm

I=1/2x,O=x

As it is a convex mirror v will be positive and u and f will be negative

(v=distance of image

U=distance of object)

M=I/O

M=(1/2x)*x

M=1/2

M=-(v/u)

1/2=-(v/-u)

1/2=v/u

u=2v

(1/f)=(1/v)+(1/u)

(1/18)=(1/v)+(1/-2v)

(1/18)=(1/v)-(1/2v)

(1/18)=(2-1/2v)

(1/18)=(1/2v)

2v=18 cm

u=18cm ans (2v=u)

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