Question

Double convex lenses are to be manufactured from a glass of refractive index $1.55$, with both faces of same radius of curvature. What is the radius of curvature required if the focal length is to be $20\, cm$?

• A. $11\,cm$
• B. $22\,cm$
• C. $7\,cm$
• D. $6\,cm$

Answer 1

Answer: (B)

$22\,cm$

Answer 2

Lens maker s formula, $\frac{1}{f} = \left(\mu-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$ Here, $f = 20 \,cm, \mu= 1.55$, $R_{1} =R$ and $R_{2} = -R$ $\therefore \frac{1}{20}=\left(1.55-1\right)\left(\frac{1}{R }-\frac{1}{\left(-R\right)}\right)$or $\frac{1}{20}=0.55\times\frac{2}{R}$ $\Rightarrow R = 1.1 \times 20$ $= 22 \,cm$