A point object is placed on the axis of a thin convex lens of focal length 0.05 m at a distance of 0.2 m from the lens and its image is formed on the axis. If the object is now made to oscillate along

Question

A point object is placed on the axis of a thin convex lens of focal length 0.05 m at a distance of 0.2 m from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of A cm , then what is the amplitude of oscillation of the image? [ you may assume, 1 + x 1 ​ ≈ 1 − x , where x << 1 ]

TestHub · Accepted Answer

According to the question, we can draw the following diagram Given, u = − 0.2 m and f = 0.05 m As we know that, f 1 ​ = v 1 ​ − u 1 ​ v 1 ​ = f 1 ​ + u 1 ​ v 1 ​ = 0.05 1 ​ − 0.2 1 ​ v 1 ​ = 5 100 ​ − 2 10 ​ v 1 ​ = 20 − 5 ⇒ v = 15 1 ​ m ​ Now, differentiating eq. (i), we get − v 2 d v ​ = − u 2 d u ​ ∴ d v = d u u 2 v 2 ​ A m a x ​ = A × ( 15 1 ​ ) 2 × ( ( − 0.2 ) 1 ​ ) 2 A m a x ​ = A × 225 1 ​ × 25 A m a x ​ = 9 A ​ ​ Here A is in cm . Hence, A m a x ​ = 9 A ​ × 1 0 − 2 m

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