Question

An object of height 2cm is placed at 20 cm distance in front of a concave mirror whose focal length is 5cm calculate height of the image

Answer 1

Answer:

Object height = 2 cm

Object image (u) = -20 cm

Focal length (f) = -5 cm

1/f = 1/u+1/v

-1/5 = -1/20+1/v

-1/5+1/20 = 1/v

(-4+1)/20 = 1/v

-3/20 = 1/v

-20/3 cm = Image distance

Linear Magnification = -(v/u)

= -(-20/3 / -20)

= - 1/3

Height of image = 1/3 * 2

= 0.66 cm

Hope this helps.

Answer 2

Given :

• Object size (hₒ) = 2 cm

• Object distance(u) = - 20 cm

[Distances are always measured from the pole of the mirror]

• focal length= -5  cm [ concave mirror]

Solution:

By applying mirror formula,

$\blacksquare \:$ 1 / f = 1 / v + 1 / u

⇒ 1 / v = 1 / f - 1 / u

⇒ 1 / v = -1 / 5 - 1 / (-20)

⇒ 1 / v = - 1 / 5 + 1 / 20

⇒ 1 / v = -4 + 1 / 20

⇒ 1 / v = -3 / 20

⇒ v = - 20/3

⇒ v = - 6.66  cm

The image is formed at a distance of 6.66 cm on the same side of the mirror.

Magnification is given by,

$\blacksquare \:$ m = - v / u = hᵢ / hₒ

Hence,

⇒ - v / u = hᵢ / hₒ

⇒ hᵢ = - v x hₒ/ u

⇒ hᵢ = - (-6.66) x 5 / - 20

⇒ hᵢ = 33.3 / - 20

⇒ hᵢ = - 1.665 cm

The height of the image is 1.665 cm.

The image formed is real and inverted.