Question

The size of the real image produced by a convex lens of focal length \(F\) is \(m\) times the size of the object. The image distance from the lens is

• A. \(F(m-1)\)
• B. \(\dfrac{(m-1)}{F}\)
• C. \(F(m+1)\)
• D. \(\dfrac{F}{(m-1)}\)

Hint:

Always use magnification along with lens formula to eliminate one variable.

Answer 1

The Correct Option is C

Step 1: Magnification relation.
For a thin lens, linear magnification is
\[ m = \frac{v}{u} \]
Step 2: Lens formula.
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Step 3: Express \(u\) in terms of \(v\).
\[ u = \frac{v}{m} \]
Step 4: Substitute in lens formula.
\[ \frac{1}{f} = \frac{1}{v} + \frac{m}{v} = \frac{m+1}{v} \]
Step 5: Solve for image distance.
\[ v = f(m+1) \]
Step 6: Conclusion.
The image distance is \(F(m+1)\).