An object is placed at a distance of 12 cm from a concave mirror of radius of curvature 16 cm .find the position of the mirror.

Bhadia

To find the position of the mirror, we need to understand how the radius of curvature and the object distance relate to each other in the case of concave mirrors.

In a concave mirror, the radius of curvature (R) is positive if the mirror is converging (concave) and negative if the mirror is diverging (convex).

The relation between the object distance (do), image distance (di), and the radius of curvature (R) is given by the mirror formula:

(1/f) = (1/do) + (1/di)

where f is the focal length of the mirror.

The focal length of a concave mirror is half the radius of curvature: f = R/2

In this case, the radius of curvature (R) is given as 16 cm. Therefore, the focal length (f) is:

f = R/2 = 16/2 = 8 cm

Now we can proceed to find the position of the mirror by applying the mirror formula.

Let's substitute the known values:
(1/f) = (1/do) + (1/di)

Substituting f = 8 cm:
(1/8) = (1/12) + (1/di)

Rearranging the equation to solve for the image distance (di):
1/di = (1/8) - (1/12)

Taking the reciprocal of both sides:
di = 1 / ((1/8) - (1/12))

Calculating the value:
di = 24 cm

Therefore, the position of the mirror (image distance) is 24 cm.