A parallel beam of light is allowed to fall on a transparent… | JEE Main 2022 (29 Jun, Shift 1)

Q63JEE Main 2022 · 29 JUN · SHIFT 1Medium

Spherical Surfaces & Thin Lenses

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is _____________ mm.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 225

Sphere radius $R = 15$ cm, $\mu = 1.5$ . First surface ( $u = \infty$ ): $\frac{1.5}{v_1} = \frac{0.5}{15} \Rightarrow v_1 = 45$ cm.
This is $45 - 30 = 15$ cm beyond the second surface, so for it $u_2 = +15$ cm, $R_2 = -15$ cm.
$\frac{1}{v_2} - \frac{1.5}{15} = \frac{1 - 1.5}{-15} \Rightarrow \frac{1}{v_2} = \frac{1}{30} + \frac{1}{10} \Rightarrow v_2 = 7.5$ cm
Distance from centre $= 15 + 7.5 = 22.5$ cm (same as $\frac{\mu R}{2(\mu - 1)}$ ).
So the answer is 225 mm.

Report a mistake

More questions on Spherical Surfaces & Thin Lenses

The power of a lens (biconvex) is 1.25 m⁻¹ in particular medium. Refractive index of the…JEE Main 2022 (28 Jul, Shift 2)
The minimum distance between an object and its real image formed by a convex lens of…MHT CET 2022 (11 Aug, Shift 2)
In an experiment with a convex lens, The plot of the image distance (v') against the…JEE Main 2022 (28 Jul, Shift 2)
The graph between 1/u and 1/v for a thin convex lens in order to determine its focal…JEE Main 2022 (26 Jul, Shift 1)
A convex lens is dipped in a liquid whose refractive index is equal to refractive index…MHT CET 2021 (21 Sep, Shift 2)
The refractive index of a converging lens is 1.4. What will be the focal length of this…JEE Main 2021 (16 Mar, Shift 2)
A convex lens of focal length f is used to form an image whose size is one fourth that of…MHT CET 2021 (20 Sep, Shift 2)
A convex lens of focal length 'F' produces a real image 'n' times the size of the object…MHT CET 2021 (20 Sep, Shift 1)

Spherical Surfaces & Thin Lenses question from JEE Main 2022 (29 Jun, Shift 1)

More questions on Spherical Surfaces & Thin Lenses