Question

At what distance from a concave mirror of focal length 10 cm should an object be placed so that:

1. its real image is formed 20 cm from the mirror?
2. its virtual image is formed 20 cm from the mirror?

Answer 1

According to the Cartesian sign convention:

Focal length of a concave mirror (f) = −10 cm

Object distance (u) is always negative since it is placed in front of the mirror.

a. For a real image, the image is formed in front of the mirror, so the image distance (v) is negative.

Image distance (v) = −20 cm

By using the mirror formula:

`1/f = 1/v + 1/u`

⇒ `1/-10 = 1/-20 + 1/u`

⇒ `1/u = 1/-10 + 1/20`

⇒ `1/u = -1/10 + 1/20`

⇒ `1/u = (-2 + 1)/20`

⇒ `1/u = -1/20`

⇒ u = −20 cm

The negative sign indicates that the object is placed in front of the mirror.

b. For a virtual image, the image is formed behind the mirror, so the image distance (v) is positive.

Image distance (v) = +20 cm

By using the mirror formula:

`1/f = 1/v + 1/u`

⇒ `1/-10 = 1/20 + 1/u`

⇒ `1/u = 1/-10 - 1/20`

⇒ `1/u = -1/10 - 1/20`

⇒ `1/u = (-2 - 1)/20`

⇒ `1/u = -3/20`

⇒ u = `-20/3`

⇒ u = −6.67 cm