Question

A convex lens has a focal length of 10 cm. If u is the object distance, then the image distance is given by

• A. \(\frac{u}{u-10}\)
• B. \(\frac{10}{u-10}\)
• C. \(\frac{10u}{u-10}\)
• D. \(\frac{u-10}{10u}\)

Answer 1

The Correct Option is C

Step 1: Recall the lens formula.

The lens formula is given by:

\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u}. \]

Rearranging for \( v \):

\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u}. \]

Simplify:

\[ v = \frac{fu}{u - f}. \]

Step 2: Substitute the given values.

The focal length is \( f = 10 \, \text{cm} \). Substituting into the formula:

\[ v = \frac{10u}{u - 10}. \]

Final Answer: The image distance is \( \mathbf{\frac{10u}{u - 10}} \), which corresponds to option \( \mathbf{(3)} \).