Question

A convex mirror has a focal of 16 cm . the image of an object kept in front of the mirror is twice the height of the object what is the distance of the object from the mirror​

Answer 1

Explanation:

It is given that,

Focal length

f=−20cm

$h1 = 3ho$

The image is three times the size of the object. So there are two cases.

Case 1. For real image

$m = - \frac{v}{u } = - 3$

Using Mirror Formula :

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

$\frac{1}{ - 20} = \frac{1}{3u} + \frac{1}{u}$

$u = \frac{ - 80}{3} \: cm$

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Answer 2

It is given that,

Focal length

f=−20cm

h

i

=3h

o

The image is three times the size of the object. So there are two cases.

Case 1. For real image

m=−

u

v

=−3

v=3u

Using mirror’s formula

f

1

=

v

1

+

u

1

−20

1

=

3u

1

+

u

1

u=

3

−80

cm

Case 2. For virtual image

m=

u

−v

=+3

v=−3u

Again using mirror’s formula

−20

1

=

−3u

1

+

u

1

u=

3

−40

cm

The possible values of u are

3

−80

cmand

3

−40

cm.