question_answer

The diameter of a Plano-convex lens is 6 cm and the thickness at the center is 3 mm. If the speed of light in the material of the lens is \[2\times {{10}^{8}}\,m/s,\]the focal length of the lens is

A) 15 cm             

B) 20 cm 

C)      30 cm             

D)      10 cm

Correct Answer: C

Solution :

\[A{{C}^{2}}=A{{E}^{2}}+C{{E}^{2}}\]or \[{{R}^{2}}={{a}^{2}}+{{(R-t)}^{2}}={{a}^{2}}+{{R}^{2}}-2Rt+{{t}^{2}}\] or \[2Rt\left\{ 1-\frac{t}{2R} \right\}={{a}^{2}}\] since \[t<\,<R,\]the term \[t/2R\]can be neglected. 2R \[t={{a}^{2}}\]        \[\therefore \]\[R=\frac{{{a}^{2}}}{2t}=15\,cm.\] \[\mu =\frac{c}{v}=1.5\]\[\therefore \]\[\frac{1}{f}=(\mu -1)\times \frac{1}{R}\] \[=(1.5-1)\times \frac{1}{15}=\frac{1}{30}\] Hence, the correction option is (c).