Question

A 10 cm long stick is kept in front of a concave mirror having a focal length of 10 cm in such a way that the end of the stick closest to the pole is at a distance of 20 cm. What will be the length of the image?

Answer 1

Given:

Object distance u = −20 cm

Focal length f = −10 cm

Height of object h₁ = 10 cm

Using the mirror formula and magnification relation,

`1/"f" = 1/"v" + 1/"u"`   ...(mirror formula)

`1/(- 10) = 1/"v" + 1/(- 20)`

`1/"v" = 1/20 - 1/10`

`1/"v" = (10 - 20)/200`

`1/"v" = (- 10)/200`

`1/"v" = (- 1)/20`

∴ v = -20 cm

Magnification formula:

M = `"h"_2/"h"_1 = -("v")/"u"`

∴ `"h"_2/"h"_1 = - ((-20))/((- 20))`

∴ `"h"_2/10 = - ((-20))/((- 20))`

∴ h₂ = −1 × 10

∴ h₂ = −10 cm

∴ length of the image will be 10 cm and the image will be formed in front of a concave mirror its nature will be Real and Inverted.