Read the following passage and answer the questions.
In a school workshop, Riya takes a long glass rod of refractive index 1.5. She grinds one end of the rod into a convex spherical surface of radius of curvature 10 cm. The centre of curvature lies inside the glass. She places a small lamp in air on the axis of the rod, facing the curved end. Then she moves the lamp to different distances from this end. For some positions, the light comes to a focus inside the glass. For other positions, the light spreads out inside the rod. Next, she cuts a thin disc from the curved end and polishes its back face flat. This gives her a thin plano-convex lens. From the same glass, she also grinds a thin double convex lens with both faces of radius 10 cm, and a thin double concave lens. Her teacher asks her to explain what she sees with the relation for refraction at a single spherical surface and the lens maker’s formula.
Riya uses the Cartesian sign convention for the radii of curvature in the lens maker’s formula. \(R_1\) is the radius of the face that the light meets first, and \(R_2\) is that of the second face. Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Double convex lens | (I) \(R_1\) infinite, \(R_2\) negative |
| (B) Double concave lens | (II) \(R_1\) positive, \(R_2\) negative |
| (C) Plano-convex lens with its curved face towards the light | (III) \(R_1\) positive, \(R_2\) infinite |
| (D) Plano-convex lens with its flat face towards the light | (IV) \(R_1\) negative, \(R_2\) positive |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
In the Cartesian sign convention, a radius is positive when the centre of curvature lies on the side to which the light travels. It is negative when the centre lies on the side from which the light comes. A flat face has an infinite radius.
(A) Double convex lens — This matches (II). The first face curves out towards the light, so its centre is beyond the lens and \(R_1\) is positive. The second face curves out away from the light, so its centre is on the incoming side and \(R_2\) is negative.
(B) Double concave lens — This matches (IV). Both faces curve the other way, so \(R_1\) is negative and \(R_2\) is positive.
(C) Plano-convex lens with its curved face towards the light — This matches (III). The curved face is met first and its centre lies beyond the lens, so \(R_1\) is positive. The flat second face gives an infinite \(R_2\).
(D) Plano-convex lens with its flat face towards the light — This matches (I). Now the flat face is met first, so \(R_1\) is infinite. The curved face comes second, with its centre on the incoming side, so \(R_2\) is negative.
NCERT (2026-27):
Sign convention – “… The distances measured in the same direction as the incident light are taken as positive and those measured in the direction opposite to the direction of incident light are taken as negative …”
Refraction by a lens – “… By the sign convention, BC1 = + R1, DC2 = –R2”
Refraction by a lens – “… Note that the formula is true for a concave lens also. In that case R1 is negative, R2 positive and therefore, f is negative.”