Q142 / 160 · TS EAMCET 2022 (20 Jul Shift 1) · Physics

What is the refractive index of the material of a double convex lens having radii of curvature of $5 \mathrm{~cm}$ and $10 \mathrm{~cm}$ and focal length of $\frac{20}{3} \mathrm{~cm}$

  • Correct answer
    A
    1.5
  • B
    2.0
  • C
    2.4
  • D
    2.6

Solution

By len's maker formula $$ \begin{aligned} & \frac{1}{\mathrm{f}}=(\mu-1)\left(\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right) \\ & \Rightarrow \quad \frac{3}{20}=(\mu-1)\left(\frac{1}{5}-\frac{1}{-10}\right) \\ & \Rightarrow \quad \frac{3}{20}=(\mu-1)\left(\frac{6+3}{30}\right) \\ & \Rightarrow \mu-1=\frac{3}{20} \times \frac{30}{9} \\ & \Rightarrow \mu-1=\frac{1}{2} \Rightarrow \mu=\frac{3}{2} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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