Image formation from lenses where object is being moved
Example: A thin converging lens of focal length f=25cm forms the image of an object on a screen placed at a distance of 75cm from the lens. The screen is moved closer to the lens by a distance of 25cm. Find the distance through which the object has to be shifted so that its image on the screen is sharp again.
Solution: Focal length of the converging lens: f=25cm Case 1: Image distance: v=75cm. Let object distance be u. Using v1−u1=f1, we get: 751−u1=251 or, u=37.5cm This means that the object is at a distance of 37.5cm from the lens initially. Case 2: The screen is shifted by 25cm towards the lens. New image distance: v=75−25=50cm Let new object distance be u Using: v1−u1=f1, we get: 501−u1=251 or, u=50cm So, the object has to be shifted by a distance: d=50−37.5=12.5cm away from the lens.