Question

The focal length of convex lens A is $15cm$ and B is $20cm$ and are placed at $5cm$ apart. Rays from an object at infinity falls on lens A. Find the magnitude of image distance from lens A.

• A. $15cm$
• B. $5cm$
• C. $\frac{20}{3}cm$
• D. $\frac{35}{3}cm$

Answer 1

The correct option is D $\frac{35}{3}cm$

Given:
Focal length of convex lens A, $f_1=15cm$
Focal length of convex lens B, $f_2=20cm$
(taken positive as per cartesian sign convention)

From defintion of focal length, image of lens A will be formed at it's focus. Hence, first image is formed at a distance of $15cm$ from it towards the right.
Distance between lenses A and B is $5cm$.
Hence, object distance for lens A would be:
$u_2=15-5=10cm$
Note that this would be positive as it is to the right of the lens. Such cases are known as virtual object.

Using lens formula for lens B,
$\frac{1}{v_2}-\frac{1}{u_2}=\frac{1}{f_2}$
$\frac{1}{v_2}-\frac{1}{10}=\frac{1}{20}$
$v_2=\frac{20}{3}cm$

Distance from lends A is:
$d=v_2+5$
$d=\frac{35}{3}$