Question

For object placed at a certain distance in front of convex mirror, the magnification is 0.8. If
the focal length of the convex mirror is 20cm then the distance of the object from the mirror__cm??

Answer 1

Given :-

◉ The magnification of a conver mirror, m = 0.8

• Focal length, f = +20 cm

To Find :-

◉ Distance of the object from the mirror, u

Solution :-

Magnification of a spherical mirror is negative of ratio of image distance and object distance.

It is also equal to the ratio of image height and object distance.

We have,

⇒ m = -v/u

⇒ 0.8 = -v/u

⇒ v = -0.8u ...(1)

Also, We know

⇒ 1/f = 1/v + 1/u

⇒ 1 / 20 = -1 / 0.8u + 1/u [ from (1) ]

⇒ 1/20 = (0.8 - 1) / 0.8u

⇒ 1/20 = -0.2 / 0.8u

⇒ 1/20 = -1/4u

⇒ 1/5 = -1/u

⇒ u = -5 cm

Hence, The distance of the object from the convex mirror is 5 cm.

Some Information :-

☛ Focal length of a convex mirror is always positive. While, Focal length of a convex mirror is always negative.

Sign convention :-

◉ Measurements taken against the direction of incident rays is taken negative while measurements taken in the direction of incident rays is taken positive.

◉ Measurements taken below the principle axis is taken negative while those taken above the principle axis is taken negative.