Q115 / 150 · MHT CET 2020 (15 Oct Shift 2) · Physics
A glass convex lens is of refractive index $1 \cdot 55$ with both faces of same radius of curvature. What will be the radius of curvature if focal length is to be $20 \mathrm{~cm}$ ?
- Correct answerA$22 \mathrm{~cm}$
- B$21 \mathrm{~cm}$
- C$18 \mathrm{~cm}$
- D$20 \mathrm{~cm}$
Solution
Lens maker's formula,
\(\frac{1}{\mathrm{f}}=(\mu-1)\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)\)
Here, \(\mathrm{f}=20 \mathrm{~cm}, \mu=1.55, \mathrm{R}_{1}=\mathrm{R}, \mathrm{R}_{2}=-\mathrm{R}\)
\(\begin{aligned}
&\frac{1}{20}=(1.55-1)\left(\frac{1}{R}-\frac{1}{(-R)}\right) \text { or } \frac{1}{20}=0.55 \times \frac{2}{R} \\
&\Rightarrow R=1.1 \times 20=22 \mathrm{~cm}
\end{aligned}\)
Hence, the correct answer is option: 'A'.