Question

You are given two identical plano-convex lenses. When you place an object $20cm$ to the left of a single plano-convex lens, the image appears $40cm$ 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 $20cm$ to the left of this new lens, What is the approximate location of the image?

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

Answer 1

The correct option is A $10cm$ to the right of the lens

for plano convex lens

$u=-20$ ; $v=+40$ ; $f=2R$ ( R is radius of curved surface)

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{40}+\frac{1}{20}=\frac{1}{2R}$

$R=\frac{20}{3}$

for the convex lens

$u=-20$ ; $f=R=\frac{20}{3}$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}+\frac{1}{20}=\frac{3}{20}$

$v=+10$

option $A$ is correct