Question

You are given two thin identical plano-convex lenses. When you place an object 20 cm to the left of a single plano-convex lens, the image appears 40 cm to the right of the lens. You then arrange the two plano-convex lenses back to back to form a double convex lens. If the object is at $20\text{cm}$ to the left of this new lens, what is the approximate location of the image ? Given $f=2R$ for plano-convex lens

• A. 6.7 cm to the right of the lens
• B. 10 cm to the right of the lens
• C. 20 cm to the right of the lens
• D. 80 cm to the right of the lens

Answer 1

The correct option is B 10 cm to the right of the lens

For plano convex lens -
$u=-20\text{cm}$, $v=+40\text{cm}$, $f=2R$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ (lens formula)
$\frac{1}{40}+\frac{1}{20}=\frac{1}{2R}$
$R=\frac{20}{3}$
For the convex lens
$u=-20\text{cm}$, $f=R=\frac{20}{3}$
Using lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{20}=\frac{3}{20}$
$\frac{1}{v}=\frac{3}{20}-\frac{1}{20}$
$\frac{1}{v}=\frac{3-1}{20}=\frac{2}{20}$
$v=10\text{cm}$

Why this question? Concept: $\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$ is the formula for finding focal length for all kinds of lenses placed in air.