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.
The two foci of the thin double convex lens made by Riya
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → lie on opposite sides, at equal distances from the optical centre
A thin lens has two foci, one on each side. Which of them is called the first focal point depends only on the side from which the light comes.
Option (1) lie on the same side of the lens, one behind the other — Incorrect. Light can come from either side of a lens, so it has a focus on each side. Both foci cannot lie on one side.
Option (2) lie on opposite sides, with the first focal point nearer to the lens — Incorrect. For a thin lens, both foci are at the same distance f from the lens. So the first focal point is not nearer.
Option (3) lie on opposite sides, with the second focal point nearer to the lens — Incorrect. The focal length of a thin lens is the same on both sides. So the second focal point is not nearer either.
Option (4) lie on opposite sides, at equal distances from the optical centre — Correct. The foci F and F′ lie on opposite sides of the lens, and both are at a distance f from the optical centre.
NCERT (2026-27):
Refraction by a lens – “… A lens has two foci, F and F′, on either side of it …”
Refraction by a lens – “It is worth mentioning that the two foci, F and F′, of a double convex or concave lens are equidistant from the optical centre. The focus on the side of the (original) source of light is called the first focal point, whereas the other is called the second focal point.”