question_answer

A plano convex lens of refractive index \[{{\mu }_{1}}\] and focal, length \[{{f}_{1}}\] is kept in contact with another piano concave lens of refractive index \[{{\mu }_{2}}\]and focal length\[{{f}_{2}}\]. If the radius of curvature of their spherical faces is R each and \[{{f}_{1}}\,=\,2{{f}_{2}}\], then \[{{\mu }_{1}}\,and\,\,{{\mu }_{2}}\] are related as- [JEE Main Online Paper (Held On 10-Jan-2019 Morning]

A) \[3{{\mu }_{2}}-2{{\mu }_{1}}=1\]                 

B) \[{{\mu }_{1}}+{{\mu }_{2}}=3\]

C) \[2{{\mu }_{1}}-{{\mu }_{2}}=1\]                   

D)   \[2{{\mu }_{2}}-{{\mu }_{1}}=1\]

Correct Answer: C

Solution :

\[{{f}_{1}}=2{{f}_{2}}\] \[\frac{1}{{{f}_{1}}}\,=\,\left( \frac{{{\mu }_{1}}-1}{1} \right)\frac{1}{R}\] \[\frac{1}{{{f}_{2}}}\,=\,\left( \frac{{{\mu }_{2}}-1}{1} \right)\left( -\frac{1}{R} \right)\] \[{{f}_{2}}=\,-\frac{R}{{{\mu }_{2}}-1};\,\,\,\,\,\,{{f}_{1}}\,=\,\frac{R}{{{\mu }_{2}}-1}\] \[{{f}_{1}}=\,2{{f}_{2}}\] \[\frac{R}{{{\mu }_{1}}-1}\,\,=\,\,\frac{2R}{{{\mu }_{2}}-1}\] \[{{\mu }_{2}}-1\,\,=\,\,\,2{{\mu }_{1}}-2\] \[1\,\,=\,\,2{{\mu }_{1}}\,-\,\,{{\mu }_{2}}\]