Plane surface of a thin plano-convex lens reflects 50% of light, while the curved surface is completely transparent. If final image of O after refraction through lens coincides with the image formed due to partial reflection from plane surface, and distance (in m) between O and lens is x, then find x/4. (Radius of curvature = 300 cm, refractive index = 3/2.)
Physics · Mixed Chapter
JEE Mains

Question

Plane surface of a thin plano-convex lens reflects 50% of light, while the curved surface is completely transparent. If final image of O after refraction through lens coincides with the image formed due to partial reflection from plane surface, and distance (in m) between O and lens is x, then find x/4. (Radius of curvature = 300 cm, refractive index = 3/2.)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The lens is thin plano-convex with one plane face and convex radius R=300 cm=3 m. With n=3/2, lensmaker's formula gives 1/f=(n−1)/R, so f=6 m. Step 2: Reflection at the plane face produces a virtual image at a distance x behind that face. The transmitted light forms a real image at that same distance behind the thin lens when 1/f=1/x+1/x=2/x. Step 3: x=2f=12 m; hence x/4=3.