Question

A concave mirror of focal length 12cm forms double the image of an object. Find out two positions of the object when such situation is possible. Explain as well.​

Answer 1

Given: Focal length of concave mirror is f=12 cm.

Image formed is double the object.

To find : Two possible positions of object

Step by step solution :

As image formed is double the object magnification may be +2 or -2

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

Substitute ${m=2}$

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

${{v=-2u} \atop$

Spherical mirror formula is $\frac{1}{f}=\frac{1}{u} +\frac{1}{v}$

$\frac{1}{12} = \frac{1}{u} +\frac{1}{-2u}$

$\frac{1}{12} = \frac{2-1}{2u}$

$\frac{1}{12} = \frac{1}{2u}$

${2u=12}$

${u=6 cm}$

$m=\frac{-v}{u}$ and substitute ${m=-2}$

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

${v=2u}$

Spherical mirror formula is   $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

$\frac{1}{12} = \frac{1}{u} +\frac{1}{2u}$

$\frac{1}{12} =\frac{2+1}{2u}$

$\frac{1}{12} = \frac{3}{2u}$

${2u=36}$

${u=18} cm$

Hence the two possible positions of object are 6cm and 18cm

Answer 2

Answer:

Given: Focal length of concave mirror is f=12 cm.

Image formed is double the object.

To find : Two possible positions of object

Step by step solution :

As image formed is double the object magnification may be +2 or -2

m = -\frac{v}{u}m=−

u

v

Substitute {m=2}m=2

2 = -\frac{v}{u}2=−

u

v

{{v=-2u} \atop

Spherical mirror formula is \frac{1}{f}=\frac{1}{u} +\frac{1}{v}

f

1

=

u

1

+

v

1

\frac{1}{12} = \frac{1}{u} +\frac{1}{-2u}

12

1

=

u

1

+

−2u

1

\frac{1}{12} = \frac{2-1}{2u}

12

1

=

2u

2−1

\frac{1}{12} = \frac{1}{2u}

12

1

=

2u

1

{2u=12}2u=12

{u=6 cm}u=6cm

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

u

−v

and substitute {m=-2}m=−2

-2 = \frac{-v}{u}−2=

u

−v

{v=2u}v=2u

Spherical mirror formula is \frac{1}{f} = \frac{1}{u} + \frac{1}{v}

f

1

=

u

1

+

v

1

\frac{1}{12} = \frac{1}{u} +\frac{1}{2u}

12

1

=

u

1

+

2u

1

\frac{1}{12} =\frac{2+1}{2u}

12

1

=

2u

2+1

\frac{1}{12} = \frac{3}{2u}

12

1

=

2u

3

{2u=36}2u=36

{u=18} cmu=18cm