A point object is situated on the principal axis of a convex lens ( f = 15 cm ) at a distance of 30 cm from it. On the opposite side of the lens, a glass plate ( = 1.50 ) of thickness 1 cm is positioned perpendicular to the axis. Determine the distance of the final image of the point object from the lens.

Step-by-step solution

For the convex lens, the object distance is u = -30 cm and the focal length is f = +15 cm . Using the lens formula: 1 v - 1 u = 1 f 1 v - 1 -30 = 1 15 1 v = 1 15 - 1 30 = 1 30 v = 30 cm The lens forms an image at a distance of 30 cm on the opposite side. When a glass plate is placed in the path of the converging rays, it produces a shift in the position of the image in the direction of the incident light. The shift is given by: x = t (1 - 1 ) Substituting t = 1 cm and = 1.5 = 3 2 : x = 1 (1 - 2 3 ) = 1 3 cm 0.33 cm