Question

a convex mirror has a focal length of 18cm the image of an object kept in front of the mirror is half the height of an object what is the distance of the object from the mirror

Answer 1

let the height of object be 'x'. then height of image =x/2.

now using magnification formula h'/h= (-v/u).

we get x/x/2= (-v/u)

=>2 = -v/u

=> v = (-2u)

now use the mirror formula

1/v+1/u=1/f

substitute the values of f and v

-1/2u+1/u=1/18

u-2u/-2u^2=1/18              (taking LCM)

-18u= -2u^2

u=9cm

v= -18cm

Answer 2

The distance of the object from the mirror is 54 cm.

Explanation:

Given :

A convex mirror has focal length of 18 cm. The image of an object kept in front of the mirror is half of the height of the object.

To find : What is the distance of the object from the mirror?

Solution :

A convex mirror has focal length of 18 cm.

Let the object placed at O=x cm.

The image of an object kept in front of the mirror is half of the height of the object.

So, Image is at $I=\frac{x}{2}cm$

The formula to find the relationship is

$\frac{I}{O}= \frac{v}{u}$

$\frac{\frac{x}{2}}{x}= \frac{v}{u}$

$v= \frac{u}{2}$

Again the focal length formula is

$\frac{1}{f}= \frac{1}{u}+\frac{1}{v}$

Substitute the values,

$\frac{1}{18}= \frac{1}{u}+\frac{1}{\frac{u}{2}}$

$\frac{1}{18}= \frac{1}{u}+\frac{2}{u}$

$\frac{1}{18}= \frac{3}{u}$

Cross multiply,

$u=3\times 18$

$u=54$

Therefore, The distance of the object from the mirror is 54 cm.✅

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