Question

If the object is placed at a point A which is 35 cm in front of a mirror and an image is formed at the same point A from the mirror. What is the focal length of the mirror?

Answer 1

Step-by-step explanation:

Magnification =

u

−v

where, v= image distance and u= object distance.

We then have:

−v

1

=−3×−x⇒v

1

=−3x

−v

2

=2(x+5)⇒v

2

=−2x−10.

By the mirror formula, we have:

⇒

u

1

1

+

v

1

1

=

f

1

=

u

2

1

+

v

2

1

⇒

x

1

+

3x

1

=

x+5

1

+

2x+10

1

⇒

3x

4

=

2x+10

3

⇒8x+40=9x

⇒x=40

⇒

f

1

=

u

1

1

+

v

1

1

=

x

1

+

3x

1

=

3x

4

=

30

1

⇒f=30cm

Thus, the focal length of the mirror is 30cm.