question_answer

Diameter of a plano - convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is\[2\times {{10}^{8}}m/s,\] the focal length of the lens is:     AIEEE Solevd Paper-2013

A) 15 cm                   

B) 20 cm   

C)        30 cm   

D)        10 cm

Correct Answer: C

Solution :

\[{{\left( r-\frac{3}{10} \right)}^{2}}+{{3}^{2}}={{r}^{2}}\] \[{{r}^{2}}-\frac{6r}{10}+\frac{9}{10}+9={{r}^{2}}\] \[-\frac{6r}{10}+\frac{909}{100}=0\] \[r=15.15\text{ }m\] \[\frac{1}{f}=(\mu -1)\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\] \[{{R}_{plane}}=\infty \] \[{{R}_{convex}}=15\text{ }cm\] (approx.) \[\mu =\frac{3\times {{10}^{8}}}{2\times {{10}^{8}}}=\frac{3}{2}\] \[\frac{1}{f}=\frac{1}{2}\times \frac{1}{15}\] \[f=30\text{ }cm\]