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JEE Main 2021 (17 Mar, Shift 1) · Spherical Surfaces & Thin Lenses

Spherical Surfaces & Thin Lenses question from JEE Main 2021 (17 Mar, Shift 1)

Q78JEE Main 2021 · 17 MAR · SHIFT 1Medium

Spherical Surfaces & Thin Lenses

The thickness at the centre of a plano-convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 ×\times 108 ms−1{}^{-1}, the focal length of the lens is ____________.

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Answer: (b)

  1. μ=cv=3×1082×108=1.5\mu = \frac{c}{v} = \frac{3 \times 10^8}{2 \times 10^8} = 1.5
  2. Sag relation with r=3r = 3 cm, t=0.3t = 0.3 cm: R≈r22t=90.6=15R \approx \frac{r^2}{2t} = \frac{9}{0.6} = 15 cm.
  3. Plano-convex: f=Rμ−1=150.5=30f = \frac{R}{\mu - 1} = \frac{15}{0.5} = 30 cm
  4. So the answer is (b) 30 cm.
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