JEE Main 2025 Jan 29 Shift 2, Physics Q7: Thin Lens and Mirrors

JEE Main2025Jan 29, Shift 2Physics

Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts $L_{1}, L_{2}$ by $A B$ plane and $L_{3}, L_{4}$ by $X Y$ plane as shown in figure respectively. The ratio of focal lengths of lenses $L_{1}$ and $L_{3}$ is

A
$1 : 4$
B
$1 : 1$
C
$2 : 1$
D
$1 : 2$

Solution

Cutting along the principal axis ( $A B$ ) preserves both refracting surfaces of the lens, so each half $L_{1}$ (and $L_{2}$ ) is optically equivalent to the original lens with the same radii. Its focal length is unchanged: $f_{L_{1}} = f$ .

Cutting perpendicular to the principal axis ( $X Y$ ) gives two plano-convex pieces, each with only one curved surface of radius $R$ . By the lensmaker's equation,

Original: $\frac{1}{f} = (μ - 1) (\frac{2}{R})$ .

Half: $\frac{1}{f _{L_{3}}} = (μ - 1) (\frac{1}{R}) = \frac{1}{2 f}$ , so $f_{L_{3}} = 2 f$ .

$∴ \frac{f _{L_{1}}}{f _{L_{3}}} = \frac{f}{2 f} = \frac{1}{2}$ , i.e. $1 : 2$ .

Concept behind this question

Thin Lens and MirrorsNotes, formulas and examples →

Practice more Physics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2025 Jan 29 Shift 2, Physics Q7: Thin Lens and Mirrors

Concept behind this question

More previous year questions on Thin Lens and Mirrors

Practice more Physics