A thin converging lens of focal length f=25 ~cm forms the image of an object on a screen placed at a distance of 75 ~cm from the lens. The screen is moved closer to the lens by a distance of 25 ~cm . The distance through which the object has to be shifted, so that its image on the screen in sharp again is

Step-by-step solution

According to the first condition, aligned f & =25 ~cm , v=75 ~cm u & =? 1 f & = 1 v - 1 u 1 25 & = 1 75 - 1 u 1 u & = 1 75 - 1 25 1 u & = 1-3 75 u & =- 75 2 =-37.5 ~cm aligned According to the second condition aligned v₁=50 ~cm , f & =25 ~cm , u₁=? 1 f & = 1 v₁ - 1 u₁ 1 25 & = 1 50 - 1 u₁ 1 u₁ & = 1 50 - 1 25 1 u₁ & = 1-2 50 u₁ & =-50 ~cm aligned So, the screen is sharp again is aligned u & =u₁-u & =50-37.5 & =12.5 ~cm aligned