In the derivation of the lens maker’s formula, the equations for refraction at the two surfaces are added. Which assumption about a thin lens is used in this step?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(BI_1=DI_1\): the distances of \(I_1\) from the two surfaces are taken as equal
The derivation first finds the image \(I_1\) made by the first surface, B. That image is then the object for the second surface, D. A thin lens is used so that the two distances to \(I_1\) can be taken as one.
Option (1) \(BI_1=DI_1\): the distances of \(I_1\) from the two surfaces are taken as equal — Correct. In a thin lens, B and D are very close to each other. So \(I_1\) is at the same distance from both surfaces, and the two equations add up to a single relation.
Option (2) \(R_1=R_2\): the two surfaces are taken to have equal radii of curvature — Incorrect. The formula keeps \(R_1\) and \(R_2\) separate and works for any two radii, such as 10 cm and 15 cm.
Option (3) \(OB\to\infty\): the object is taken to be very far from the lens — Incorrect. The object at infinity is used after adding, to define the focal length \(f\). It has nothing to do with the lens being thin.
Option (4) \(n_1=n_2\): the lens and the outside medium are taken to have equal refractive index — Incorrect. If \(n_1=n_2\), the lens would not bend light at all and \(1/f\) would be zero. The derivation keeps \(n_2\) different from \(n_1\).
NCERT (2026-27):
Refraction by a lens – “… For a thin lens, BI1 = DI1. …”