A point object is moving at a constant speed of 1 ~ms ⁻¹ along the principal axis of a convex lens of focal length 10 ~cm . The speed of the image is also 1 ~ms ⁻¹ , when the object is at cm from the optical centre of the lens.

Step-by-step solution

Given, f=10 ~cm d u d t =1 ~ms ⁻¹, d v d t =1 ~ms ⁻¹ From lens formula gathered 1 f = 1 u + 1 v 1 v = 1 f - 1 u = u-f f u v= f u u-f gathered Differentiating Eq. (i) w.r.t. t , aligned d ( 1 f ) d t & = d ( 1 u ) d t + d ( 1 v ) d t 0 & =- 1 u^2 d u d t - 1 v^2 d v d t 1 u^2 d u d t =- 1 v^2 d v d t - v^2 u^2 & = d v d t d t d u aligned Putting Eq. (ii) values in the above equation, - (f u)^2 (u-f)^2 1 u^2 = d v d t d t d u (u-f)^2=f^2 d u d t d t d v Substituting given values in above equation, (u-10)^2=(10)^2 1 1