JEE Physics 2026 Question with Solution

Given: The magnitudes of powers of a biconvex lens and a plano-convex lens are equal. For the biconvex lens, refractive index is $1.5$. For the plano-convex lens, refractive index is $1.7$. The curved surface of the plano-convex lens has the same curvature as the back surface of the biconvex lens.

Find: The ratio of radii of curvature of the front and back surfaces of the biconvex lens.

Concept: The power of a thin lens in air is given by the lens-maker formula:

For a plano-convex lens, one surface is plane, so its radius of curvature is infinite.

Step 1: Power of the plano-convex lens. Let the curved surface radius be $R$. With refractive index $n=1.7$,

Step 2: Power of the biconvex lens. Let the front and back radii be $R_1$ and $R_2$. With refractive index $n=1.5$,

Step 3: Use the given condition. Since the curved surface of the plano-convex lens matches the back surface of the biconvex lens,

Also, the magnitudes of powers are equal:

Step 4: Solve for the ratio as shown in the given working:

Thus,

Therefore, the correct option is D.

The key point is to apply the lens-maker formula with the correct sign convention for the radii. For the plano-convex lens, the plane surface contributes zero curvature because its radius is infinite. Then compare the magnitude of its power with that of the biconvex lens and substitute the condition $R=R_2$. This leads to the required ratio, matching option D.