Question

The radius of curvature of concave mirror is 24 cm. Object is placed
twice of focal length before mirror then find magnification​

Answer 1

Answer:

The radius of curvature, R = -24cm

So, focal length, f = - R/2 = - 24/2 = -12 cm

Since the object distance is given twice that of the focal length before the mirror, therefore,

Object distance, u = 2 * f = 2 * (-12) = -24 cm

Let the image distance be denoted as “v” cm.

Using the mirror formula, we get

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

Rearranging the eq. and then substituting the given values, we get

⇒ 1/v = 1/f – 1/u

⇒ 1/v = 1/(-12) – 1/(-24)

⇒ 1/v = [-2 + 1] / 24

⇒ 1/v = - 1/24

⇒ v = -24 cm ← negative sign indicates that the image is located on the same side of the object before the mirror.

Thus,  

The magnification of the mirror is given as,

= - [v/u]

= - [(-24) / (-24)]

= - 1 ← negative sign indicates the image is inverted.

Answer 2

Answer:

The radius of curvature, R = -24cm

So, focal length, f = - R/2 = - 24/2 = -12 cm

Since the object distance is given twice that of the focal length before the mirror, therefore,

Object distance, u = 2 * f = 2 * (-12) = -24 cm

Let the image distance be denoted as “v” cm.

Using the mirror formula, we get

Rearranging the eq. and then substituting the given values, we get

⇒ 1/v = 1/f – 1/u

⇒ 1/v = 1/(-12) – 1/(-24)

⇒ 1/v = [-2 + 1] / 24

⇒ 1/v = - 1/24

⇒ v = -24 cm ← negative sign indicates that the image is located on the same side of the object before the mirror.

Thus,  

The magnification of the mirror is given as,

= - [v/u]

= - [(-24) / (-24)]

= - 1 ← negative sign indicates the image is inverted.