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JEE Main 2022 (24 Jun, Shift 1) · Combination of Lenses

Combination of Lenses question from JEE Main 2022 (24 Jun, Shift 1)

Q43JEE Main 2022 · 24 JUN · SHIFT 1Medium

Combination of Lenses

Two identical thin biconvex lens of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is __________ cm.

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

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Answer: 10

  1. Each glass lens: 115=0.5⋅2R⇒R=15 cm\frac{1}{15} = 0.5 \cdot \frac{2}{R} \Rightarrow R = 15\text{ cm}
  2. Liquid forms a biconcave lens: 1fl=−0.25⋅215=−130\frac{1}{f_l} = -0.25 \cdot \frac{2}{15} = -\frac{1}{30}
  3. 1F=215−130=330=110\frac{1}{F} = \frac{2}{15} - \frac{1}{30} = \frac{3}{30} = \frac{1}{10}
  4. Focal length of the combination = 10 cm.
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