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QJEEM18Ph7285: JEE Main 2018 Physics - Class 12 JEEM18Ph7285 Solution: A planoconvex lens becomes an optical system of focal length…

A planoconvex lens becomes an optical system of 2828 cmcm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.

If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig-B, it acts like an optical system of focal length 1010 cm.cm. The refractive index of the material of lens is :

JEE Main 2018 (Online) 15th April Morning Slot Physics - Geometrical Optics Question 189 English

Multiple Choice Options

  • A 1.501.50
  • B 1.551.55
  • C 1.751.75
  • D 1.511.51

Step-by-Step Verified Solution

When plane durface is silvered then focus length of lens,

f1 = R2(μ−1){R \over {2\left( {\mu - 1} \right)}}

and when curver surface is silvered then focus length of lens,

f2 = R2μ{R \over {2\mu }}

∴    \therefore\,\,\,\, f1f2=R2(μ−1)×2μR{{{f_1}} \over {{f_2}}} = {R \over {2\left( {\mu - 1} \right)}} \times {{2\mu } \over R}

μ(μ−1){\mu \over {\left( {\mu - 1} \right)}}

given f1 = 28 and f2 = 10

∴    \therefore\,\,\,\, 2810=μμ−1{{28} \over {10}} = {\mu \over {\mu - 1}}

⇒\Rightarrow     \,\,\,\, 28 μ\mu −- 28 = 10 μ\mu

⇒\Rightarrow     \,\,\,\, 18 μ\mu = 28

⇒\Rightarrow     \,\,\,\, μ\mu = 2818{{28} \over {18}} = 1.55

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