A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. When plane surface of the lens is silvered, the image is formed at 3K cm from the lens. Find the value of K.
Physics · Mixed Chapter
JEE Mains

Question

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. When plane surface of the lens is silvered, the image is formed at 3K cm from the lens. Find the value of K.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The light traverses the lens twice and reflects at its silvered plane face, whose own curvature is zero. Thus the combination behaves like a concave mirror of effective power 2/f and effective focal length fₑff=f/2=7.5 cm. Step 2: For object distance 20 cm, mirror formula gives 1/v=1/fₑff−1/u=1/7.5−1/20=2/15−1/20=1/12. Step 3: Magnitude of image distance is 12 cm=3K cm. Therefore K=4.