Question

A convex mirror of focal length 2 meter forms image of 2 cm . If the object is 10 meter away from mirror then find the position of image formed and size of object.

Answer 1

Answer:

It is to be remembered that a convex mirror always forms the virtual, erect and diminished image.

Given: Object distance, u=−10cm Focal length, f=15cm

To find: Image distance, v

From mirror formula :

v

1

+

u

1

=

f

1

v

1

−

10

1

=

15

1

v

1

=

15

1

+

10

1

=

150

25

v=6cm

Hence image will be formed 6 cm beyond the mirror, i.e virtual magnification

m=

u

−v

=

−10

−6

=0.6

Hence it will be erect and diminished.

Answer 2

Answer:

Given = focal length,f = 2 cm (taken positive because forcal length of convex mirror is behind the mirror)

image height, h' = 2 cm

object distance, u = -10 cm

We know that,

Using mirror formula,

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

$\boxed{ \frac{1}{2} = \frac{1}{v} - \frac{1}{10} }$

$\boxed{ \frac{1}{2} + \frac{1}{10} = \frac{1}{v} }$

$\boxed{ \frac{5 + 1}{10} = \frac{1}{v} }$

$\boxed{ \frac{1}{v} = \frac{6}{10} }$

$\boxed{v = \frac{10}{6} }$

$\boxed{v = 1.7 \: cm}$

Linear magnification = -v/u

=> -1.7/-10

=> 0.17

Since the magnification is positive hence the image is virtual and erect and the image size will be highly diminished.