Question

a concave mirror has focal length of 20 cm. At what distance from the mirror a 5cm tall object be placed so that it forms an image at 15 cm from the mirror ? Also calculate the size of the image formed.​

Answer 1

Answer:

According to the question,

Image distance, v=−15 cm (negative due to convex lens)

Focal length, f=−20 cm

Let the object distance be u.

By lens formula:

v

1

−

u

1

=

f

1

[4pt]

⇒

−15 cm

1

−

u

1

=

−20 cm

1

[4pt]

⇒

u

1

=

20 cm

1

+

−15 cm

1

[4pt]

⇒

u

1

=

60 cm

3−4

=

60 cm

−1

[4pt]

⇒u=−60 cm

Therefore, object is placed at 60 cm away from the lens, on the same side as image.

Now,

Height of object, h

1

=5cm

Magnification, m=

h

1

h

2

=

u

v

Putting value of v and u:

Magnification, m=

5 cm

h

2

=

−60 cm

−15 cm

⇒

5 cm

h

2

=

4

1

⇒h

2

=

4

5 cm

=1.25 cm

Thus, the height of the image is 1.25 cm and the positive sign means the image is virtual and erect.