Q75 / 90 · JEE Main 2024 (06 Apr Shift 2) · Physics

For the thin convex lens, the radii of curvature are at $15 \mathrm{~cm}$ and $30 \mathrm{~cm}$ respectively. The focal length the lens is $20 \mathrm{~cm}$. The refractive index of the material is :

  • A
    1.2
  • B
    1.8
  • Correct answer
    C
    1.5
  • D
    1.4

Solution

$\begin{aligned} & \frac{1}{\mathrm{f}}=\left(\frac{\mu_{\text {lens }}}{\mu_{\text {air }}}-1\right)\left(\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right) \\ & \Rightarrow \frac{1}{+20}=\left(\frac{\mu}{1}-1\right)\left(\frac{1}{+15}-\frac{1}{(-30)}\right) \\ & \Rightarrow \frac{1}{20}=(\mu-1)\left(\frac{3}{30}\right) \\ & \Rightarrow \mu-1=\frac{1}{2} \\ & \Rightarrow \mu=1+\frac{1}{2}=\frac{3}{2}=1 \cdot 5\end{aligned}$

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

Relevant Questions