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Question

Convex side of a plano-convex lens is fully immersed in a liquid, of same refractive index (equal to 8/5) as that of the lens. Which one among the following is correct regarding the image of a point source of light placed in air at 40 cm away from the lens? (Assume the focal length of the plano-convex lens as 20 cm)

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CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is

Its image will be formed 64 cm behind the lens

Since the liquid has the same refractive index (1.6) as the lens, the curved surface immersed in it causes no refraction at all, so only the flat surface (air to lens, n=1 to n=1.6) refracts the light. Using the flat-surface refraction relation, image distance = (n2/n1) × object distance = 1.6 × 40 = 64 cm. Hence the image forms at 64 cm, and option (c) is wrong because refraction still occurs at the flat surface.

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Important Questions from Refraction and Reflection

  1. A convex lens of focal length f will form a magnified real image of an object, if the object is placed.

  2. A ray of light travelling in the direction \(\frac{1}{2} (\hat i + \sqrt 3 \hat j)\) is incident on a plane mirror. After reflection it travels along the direction  \(\frac{1}{2} (\hat i - \sqrt 3 \hat j)\)  The angle of incidence is:

  3. Twinkling of stars is due to atmospheric

  4. An optical fibre has a core material of refractive index of 1.55 and cladding material of refractive index of 1.50. The numerical aperture of the fibre is

  5. Lenses are widely used in spectacle to

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