Question

A 5 cm tall light bulb is placed at a distance of 30 cm from a concave mirror having a focal length 0f 20 cm.

Answer 1

Answer:

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