A plano-convex lens fits exactly into a plano-concave lens as shown in the figure. Their plane surfaces are parallel to each other. The lenses are made of different materials of refractive indices 1.6 and 1.5 respectively. If R is the radius of curvature of the curved surfaces of the lenses, then t…

Question

A plano-convex lens fits exactly into a plano-concave lens as shown in the figure. Their plane surfaces are parallel to each other. The lenses are made of different materials of refractive indices 1.6 and 1.5 respectively. If R is the radius of curvature of the curved surfaces of the lenses, then the focal length of the combination is .

Accepted Answer

(4) R/(0.1). Given: plano-convex lens of index 1.6, plano-concave lens of index 1.5, common curved surface of radius R, and plane outer faces. Idea: two thin lenses in contact add their powers, 1/F=1/(f₁)+1/(f₂), and each focal length comes from the lens maker's formula 1/f=(n-1)(1/(R₁)-1/(R₂)). Plano-convex, plane face first: R₁=∞, R₂=-R, so 1/(f₁)=(1.6-1)(0+1/R)=(0.6)/R. Plano-concave, the same curved surface first: R₁=-R, R₂=∞, so 1/(f₂)=(1.5-1)(-1/R-0)=-(0.5)/R. Adding: 1/F=(0.6-0.5)/R=(0.1)/R. So F=R/(0.1), that is 10R — only the difference of the two refractive indices survives, which is why the pair is such a weak lens.

Step-by-step solution

Why the other options are wrong