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JEE Main 2023 (24 Jan, Shift 1) · Combination of Lenses

Combination of Lenses question from JEE Main 2023 (24 Jan, Shift 1)

Q38JEE Main 2023 · 24 JAN · SHIFT 1Medium

Combination of Lenses

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance x=x = _________ cm, from concave lens.

Figure

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

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Answer: 120

  1. Plano lens: ∣f∣=Rμ−1=300.75=40 cm|f| = \frac{R}{\mu - 1} = \frac{30}{0.75} = 40\text{ cm}; concave f=−40f = -40, convex f=+40f = +40.
  2. Concave lens forms a virtual image of the distant object 40 cm before it.
  3. Convex lens: u=−(40+40)=−80u = -(40 + 40) = -80: 1v=140−180⇒v=80 cm\frac{1}{v} = \frac{1}{40} - \frac{1}{80} \Rightarrow v = 80\text{ cm}.
  4. x=40+80=120 cmx = 40 + 80 = 120\text{ cm}
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