An object of length 10 cm is placed at right angles to the principal axis of a mirror of radius of curvature 60 cm such that its image is virtual, erect and has a length 6 cm . What kind of mirror it is and also determine the position of the object?

Step-by-step solution

Since the image is virtual, erect and of a smaller size, the given mirror is 'convex' (concave mirror does not form an image with the said description). Given R = + 60 cm ∴ f ⁡ = R ⁡ 2 = 3 0 cm Transverse magnification, m ⁡ = I ⁡ O ⁡ = 6 1 0 = + 3 5 Further m ⁡ = - v ⁡ u ⁡ = 3 5 ∴ v ⁡ = - 3 u ⁡ 5 Using 1 v ⁡ + 1 u ⁡ = 1 f ⁡ - 5 3 u ⁡ + 1 u ⁡ = 1 3 0 - 5 + 3 3 u ⁡ = 1 3 0 ∴ u = - 20 cm Thus the object is at a distance 20 cm ( from the pole) in front of the mirror.