Question

The distance of an object from a convexmirror is 14 m and the image is formed on the point. Find the radius and centre of curvature of the mirror.

Answer 1

It is stated that,

The distance of the object(u) = 14 m

The Distance of the formed image (v) = The distance of the object(u) = 14 m

Let, the focal length be 'f' and the length of the radius be 'r' and the center of the curvature be 'c'.

From the relationship we get that,

1/f = (1/u) + (1/v)

⇒ 1/f = (1/14) + (1/14)

⇒ 1/f =(1+1)/14 [∴ The L.C.M. of the denominators is 14]

⇒ 1/f = 2/14

⇒ 1/f = 1/7

⇒ f = 7 m

So, the focal length is 7 m.

We know that, the radius of the mirror is half to the focal length.

So, from the relationship we get that,

2r = f

⇒ 2r = 7

⇒ r = 7/2

⇒ r = 3.5 m

So, the radius of the mirror is 3.5 m.

We know that, the radius of the mirror = centre of curvature of the mirror

Hence, c = r = 3.5 m

∴ The length of the centre of curvature of the mirror is 3.5 m.

Answer 2

❇The two points should be remember in the problem is.

❇Radius of the mirror is half of the focal length.

❇Radius of the mirror is equal to centre of curvature of the mirror.

❇We got radius of the =3.5m

❇so center of curvature =3.5m

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