A spherical surface of radius of curvature R, separates air from… | JEE Main 2025 (23 Jan, Shift 1)

Q26JEE Main 2025 · 23 JAN · SHIFT 1Medium

Spherical Surfaces & Thin Lenses

A spherical surface of radius of curvature $R$ , separates air from glass (refractive index $= 1.5$ ). The centre of curvature is in the glass medium. A point object ' $O$ ' placed in air on the optic axis of the surface, so that its real image is formed at 'I' inside glass. The line OI intersects the spherical surface at $P$ and $PO = PI$ . The distance $PO$ equals to

Show answer and solution

Answer: (a)

$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$ with $\mu_1 = 1$ , $\mu_2 = 1.5$ , $R = +R$ (centre in glass).
Let $PO = PI = x$ : $u = -x$ , $v = +x$ .
$\frac{1.5}{x} + \frac{1}{x} = \frac{0.5}{R} \Rightarrow \frac{2.5}{x} = \frac{0.5}{R}$
So the answer is (a) $x = 5R$ .

Report a mistake

More questions on Spherical Surfaces & Thin Lenses

Light from a point source in air falls on a spherical glass surface (refractive index, μ…JEE Main 2025 (3 Apr, Shift 2)
A bi-convex lens has radius of curvature of both the surfaces same as 1/6 cm. If this…JEE Main 2025 (2 Apr, Shift 2)
Refractive index of a glass convex lens is 1.5. The radius of curvature of each of the…MHT CET 2025 (26 Apr, Shift 2)
A convex lens of refractive index 1.5 has power 3D. It is placed in a liquid of…MHT CET 2025 (23 Apr, Shift 2)
A concave lens (refractive index = 1.5) has both surfaces of same radius of curvature R…MHT CET 2025 (22 Apr, Shift 2)
A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal…JEE Main 2025 (24 Jan, Shift 1)
A photograph of a landscape is captured by a drone camera at a height of 18 km. The size…JEE Main 2025 (24 Jan, Shift 2)
Let u and v be the distances of the object and the image from a lens of focal length f…JEE Main 2025 (29 Jan, Shift 1)

Spherical Surfaces & Thin Lenses question from JEE Main 2025 (23 Jan, Shift 1)

More questions on Spherical Surfaces & Thin Lenses