For a certain lens, the magnification of an object when placed at a distance of 0.15 m is twice of the magnification produced, when the distance was 0.2 m . If in both the situations a real image is formed, then what is the focal length (in cm ) of the lens?

Step-by-step solution

Let as shown, 1 and 2 are positions of objects and images in two different situations. Object It is given v ₁ u ₁ = 2 v ₂ u ₂ Here, u ₁ = - 15 cm , u ₂ = - 20 cm ∴ v ₁ = 2 v ₂ × u ₁ u ₂ = 2 v ₂ × 15 20 = 3 2 v ₂ n o w , 1 f = 1 v - 1 u ∴ 1 f = 1 v ₁ - 1 u ₁ a n d 1 f = 1 v ₂ - 1 u ₂ s o , 1 v 1 - 1 u 1 = 1 v 2 - 1 u 2 ⟹ 2 2 v ₂ + 1 15 = 1 v ₂ + 1 20 ⟹ v = 20 cm ∴ v ₁ u ₁ = 2 v ₂ u ₂ = 2 × 20 20 = 2 ⟹ v ₁ = 2 u ₁ = 2 × 15 = 30 cm Therefore, 1 f = 1 v ₁ - 1 u 1 = 1 15 + 1 30 = 3 30 ∴ f = 10 cm