An object approaches a convergent lens from the left of the lens with a uniform speed 5 ~m / s and stops at the focus, the image

Step-by-step solution

From lens formula, 1 f = 1 v - 1 u Differentiating w.r.t. time, we get aligned 0 &=- 1 v² d v d t + 1 u² d u d t d v d t &= ( v² u² ) d u d t v_ i &=m² v_ O ...(i) aligned where, v_ i = image speed, v₀= object speed, and m= magnification. Again differentiating w.r.t. time, we get aligned d² v_ i d t² &=v₀ 2 m d m d t a_ i &=2 m v₀ d m d t ...(ii) aligned where, a_ i is the acceleration of the image. So, when the object approaches the lens with a uniform speed 5 ~m / s and stops at focus, then from Eq. (i) and (ii),