A double convex lens made of glass has both radii of curvature of magnitude $20 \mathrm{~cm}$. Incident light rays parallel to the axis of the lens will converge to a point at a distance ' $L$ ' from the common pole P. The value of L is [Refractive index of glass $=1.5$ ]

• A

  $10 \mathrm{~cm}$
• B

  $40 \mathrm{~cm}$
• C

  $\frac{20}{3} \mathrm{~cm}$
• Correct answer
  D

  $20 \mathrm{~cm}$

Solution

Lens maker formula: $\frac{1}{\mathrm{f}}=(\mu-1)\left(\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right)$ If incidence ray has direction left to right \& $\left|R_1\right|=\left|R_2\right|=20 \mathrm{~cm}=\mathrm{R}, \mu=1.5$, then $\begin{aligned} & \frac{I}{f}=(\mu-1)\left(\frac{1}{R}-\frac{1}{(-R)}\right)=\frac{2(\mu-1)}{R} \\ & =\frac{2(1.5-1)}{20 \mathrm{~cm}} \\ & \Rightarrow f=20 \mathrm{~cm}\end{aligned}$

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