Question

Lenses are constructed by a material of refractive index 1.50. The magnitude of the radii of curvature are 20 cm and 30 cm. Find the focal lengths of the possible lenses with the above specifications.

Answer 1

Four possible lenses,

(i) $R_1=20\text{cm}$, $R_2=30\text{cm}$

For (i) $R_1=20\text{cm}$, $R_2=-30\text{cm}$

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

$=0.5[\frac{1}{20}-\frac{1}{30}]=\frac{0.5\times 5}{60\times 10}$

$f=24\text{cm}$

For (ii) $\frac{1}{f}=\left(0.5\right)[\frac{1}{20}-\frac{1}{60}]$

$R_1=+20\text{cm}$

$R_2=+30\text{cm}$

$=\frac{0.5\times 1}{10\times 60}$

$f=120\text{cm}$

For (iii) $R_1=-20\text{cm}$ $R_2=-30\text{cm}$

$\frac{1}{f}=\left(0.5\right)[-\frac{1}{20}+\frac{1}{60}]$

f = -120

For (iv) $R_1=-20\text{cm}$, $R_2=30\text{cm}$

f = 24 cm.