An optical bench has 1.5 m long scale having four equal divisions in each c m . While measuring the focal length of a convex lens, the lens is kept at 75 c m mark of the scale and the object pin is ke

Question

An optical bench has 1.5 m long scale having four equal divisions in each c m . While measuring the focal length of a convex lens, the lens is kept at 75 c m mark of the scale and the object pin is kept at 45 c m mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 c m mark. In this experiment, the percentage error in the measurement of the focal length of the lens is_____

TestHub · Accepted Answer

Let, x 1 = d i s t a n c e o f o b j e c t f r o m O x 2 = d i s t a n c e o f l e n s f r o m O x 3 = d i s t a n c e o f i m a g e f r o m O ∴ u = x 2 - x 1 = 75 - 45 = 30 c m ⇒ ∆ u = ∆ x 2 + ∆ x 1 = 1 4 + 1 4 = 1 2 c m ⇒ error in measurement of “ u ” And, v = x 3 - x 2 = 135 - 75 = 60 c m ⇒ ∆ v = ∆ x 3 + ∆ x 2 = 1 4 + 1 4 = 1 2 c m ⇒ error in measurement of “ v ” Using Lens formula ∴ 1 v - 1 u = 1 f ⇒ 1 60 + 1 30 = 1 f ⇒ 1 f = 1 20 ∴ f = 20 c m , A l s o , - d v v 2 + - d u u 2 = - d f f 2 → [differentiating lens formula] ⇒ d f f = f d v v 2 + d u u 2 = 20 1 60 2 + 1 30 2 1 2 ∴ d f f × 100 = 10 1 36 + 1 9 = 50 36 = 1.38 a n d 1.39 b o t h

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