Question

The diameter of the aperture of a plano-convex lens is 6 cm and its maximum thickness is 3 mm. If the velocity of light in the material of the lens is $2\times {10}^{8}m/s$, its focal length is

• A. 10 cm
• B. 15 cm
• C. 30 cm
• D. 60 cm

Answer 1

The correct option is C 30 cm



$R^2=d^2+(R-t{)}^2$
$R^2-d^2=R^2{\{1-\frac{t}{R}\}}^2$
$1-\frac{d^2}{R^2}=1-\frac{2t}{R}$
$R=\frac{(3{)}^2}{2\times \left(0.3\right)}=\frac{90}{6}=15cm$
$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
$\frac{1}{f}=(\frac{3}{2}-1)\left(\frac{1}{15}\right)$
$f=30cm$