Question

Curved surfaces of a plano-convex lens of refractive index $\mu_{1}$ and a plano-concave lens of refractive index $\mu_{2}$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

• A. $\frac{1}{\mu_{2}-\mu_{1}}$
• B. $\mu_{1}-\mu_{2}$
• C. $\frac{1}{\mu_{1}-\mu_{2}}$
• D. $\mu_{2}-\mu_{1}$

Answer 1

Answer: (B)

$\frac{1}{ f _{1}}=\left(\mu_{1}-1\right)\left(\frac{1}{ R }\right)$
$\frac{1}{ f _{2}}=\left(\mu_{2}-1\right)\left(-\frac{1}{ R }\right)$
$\frac{1}{ f _{1}}+\frac{1}{ f _{2}}=\frac{1}{ f _{ eq }}=\frac{\left(\mu_{1}-1\right)-\left(\mu_{2}-1\right)}{ R }$
$\frac{1}{ f _{ eq }}=\frac{\left(\mu_{1}-\mu_{2}\right)}{ R }$
$\frac{ R }{ f _{ eq }}=\left(\mu_{1}-\mu_{2}\right)$