Question

If \(\frac{y}{4}\) and are the object and image distances due to a convex lens respectively, then its focal length is 

• A. \(\frac{5y}{4}\)
• B. \(\frac{4y}{5}\)
• C. \(\frac{3y}{4}\)
• D. \(\frac{4y}{5}\)

Answer 1

The Correct Option is C

For a convex lens, the lens formula is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Where:
\( f \) is the focal length,
\( v \) is the image distance, and
\( u \) is the object distance.
From the given data:
\( u = y \) (object distance),
\( v = \frac{y}{4} \) (image distance).
Substituting these values into the lens formula: \[ \frac{1}{f} = \frac{1}{\frac{y}{4}} - \frac{1}{y} \] Simplifying: \[ \frac{1}{f} = \frac{4}{y} - \frac{1}{y} = \frac{3}{y} \] Thus: \[ f = \frac{y}{3} \]

The correct option is (C): \(\frac{3y}{4}\)