Question

The distance between a concave mirror and the screen is 5m. An object of height 1 cm is

placed between the mirror and the screen on which an image of height 5cm is formed.

Calculate (a) the focal length, (b) the radius of curvature of the mirror and (c) the

position of the object.​

Answer 1

Given: An object of 5cm tall is placed at a distance of 10cm from a concave mirror of radius of curvature 30cm

To find: the nature, position and size of the image and draw the ray diagram to represent the above case.

Solution:

According to the given criteria,

Let height of the image be h

i

and

Height of the object, h

o

=5cm

Object distance, u=−10cm

Radius of curvature, R=−30cm

We know, focal length, f=

2

R

=

2

30

=−15cm

Now applying mirror formula, we get

f

1

=

v

1

+

u

1

⟹

v

1

=

f

1

−

u

1

⟹

v

1

=

−15

1

−

−10

1

⟹

v

1

=

150

−10+15

=

150

5

⟹v=30cm

Position of the image is behind the mirror at the distance of 30 cm

Magnification, m=−

u

v

=

h

o

h

i

⟹−

−10

30

=

5

h

i

⟹h

i

=3×5=15cm

Nature of the image formed: virtual, erect (as magnification is positive) and enlarged.

Ray diagram is as shown in above figure.

solution

Answer 2

Answer:

m=hi/ho=-v/u

-v/u=4/1

-v=4u

Explanation: