Convex side of a plano-convex lens is fully immersed in a liquid, of same refractive index (equal to 8/5) as that of the lens. Which one among the following is correct regarding the image of a point source of light placed in air at 40 cm away from the lens? (Assume the focal length of the plano-convex lens as 20 cm)
- AIts image will be formed 40 cm behind the lens
- BIts image will be formed at 25 cm behind the lens
- CNo image will be formed because of the same refractive index of the lens and the liquid
- DIts image will be formed 64 cm behind the lens
Explanation
Because the convex surface is immersed in a liquid whose refractive index (8/5) equals that of the lens, that surface has zero optical power; refraction occurs only at the plane air-glass surface. Gaussian optics then yield no real image behind the lens - only a virtual image on the object side - so the claimed '64 cm behind the lens' is physically impossible. Option (C) captures this: with the lens-liquid interface optically neutralised, no (real) image is formed. Note: the question is flawed, since a virtual image does form and 'no image' is strictly inaccurate; (C) is the intended best option. (Stored key corrected from D.)