A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm, and (b) a concave lens of focal length 16 cm?

#### Solution

In the given situation, the object is virtual and the image formed is real.

Object distance, u = +12 cm

**(a)** Focal length of the convex lens, f = 20 cm

Image distance = v

According to the lens formula, we have the relation:

`1/"v" - 1/"u" = 1/"f"`

`1/"v" - 1/12 = 1/20`

`1/"v" = 1/20 + 1/12`

= `(3 + 5)/60`

= `8/60`

∴ v = `60/8` = 7.5 cm

Hence, the image is formed 7.5 cm away from the lens, toward its right.

**(b)** Focal length of the concave lens, f = −16 cm

Image distance = v

According to the lens formula, we have the relation:

`1/"v" - 1/"u" = 1/"f"`

`1/"v" = -1/16 + 1/12`

= `(-3 + 4)/48`

= `1/48`

∴ v = 48 cm

Hence, the image is formed 48 cm away from the lens, toward its right.