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JEE Main 2025 (24 Jan, Shift 1) · Combination of Lenses

Combination of Lenses question from JEE Main 2025 (24 Jan, Shift 1)

Q15JEE Main 2025 · 24 JAN · SHIFT 1Medium

Combination of Lenses

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is

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Answer: (b)

  1. Lens in liquid: 1fL=(1.51.2−1)1R=0.25R⇒fL=4R\frac{1}{f_L} = \left(\frac{1.5}{1.2}-1\right)\frac{1}{R} = \frac{0.25}{R} \Rightarrow f_L = 4R
  2. Plane side silvered (plane mirror, no power): 1F=2fL⇒F=fL2=2R\frac{1}{F} = \frac{2}{f_L} \Rightarrow F = \frac{f_L}{2} = 2R
  3. 2R=0.2 m⇒R=0.1 m2R = 0.2\text{ m} \Rightarrow R = 0.1\text{ m}
  4. So the answer is (b) 0.10 m.
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