Question

A plano convex lens of refractive index ${\mu }_1$ and focal length $f_1$ is kept in contact with another plano 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 $f_1=2f_2$, then ${\mu }_1$ and ${\mu }_2$ are related as :

• A. ${\mu }_1+{\mu }_2=3$
• B. $2{\mu }_1-{\mu }_2=1$
• C. $2{\mu }_2-{\mu }_1=1$
• D. $3{\mu }_2-{\mu }_1=1$

Answer 1

The correct option is B $2{\mu }_1-{\mu }_2=1$

Given, $\frac{1}{2f_2}=\frac{1}{f_1}=({\mu }_1-1)(\frac{1}{\infty }-\frac{1}{-R})$

From lens makers formula, $\frac{1}{f_2}=({\mu }_2-1)(\frac{1}{-R}-\frac{1}{\infty })$

$\frac{({\mu }_1-1)}{R}=\frac{({\mu }_2-1)}{2R}$

$2{\mu }_2-{\mu }_2=1$.