Question

An object of size 4 cm placed perpendicular to
the principal axis of concave mirror at 12 cm from
the pole of the mirror. Find out the size of the
image if the radius of curvature is 20 cm.

Answer 1

Answer:

The height of the image is 20 cm and it is inverted.

Explanation:

The height of the object, h₀ = 4 cm

The object distance, u = -12 cm

The radius of curvature of the mirror, R = 20 cm

∴ The focal length of the mirror, f = R/2 = 20/2 = -10 cm

The value of the focal length of a concave mirror is always negative.

We have the mirror formula as:

1/f = 1/u + 1/v

⇒ Image distance, v = (uf) / (u - f)

                               v = (-12 × -10) / (-12 - -10)

                               v = -60 cm

We have the magnification formula as:

-v/u = h₁/h₀

Where h₁ is the height of the image.

∴ h₁ = (-v/u) × h₀

  h₁ = (- -60/-12) × 4

⇒ h₁ = -20 cm

So the height of the image is 20 cm and it is inverted (negative sign).