Question

A convex lens of focal length \( F \) produces a real image \( n \) times the size of the object. The image distance is

• A. \( F(n+1) \)
• B. \( F(n-1) \)
• C. \( \frac{F}{n+1} \)
• D. \( \frac{F}{n-1} \)

Hint:

In lens problems, use the lens formula \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) and the magnification formula \( m = \frac{v}{u} \) to find the image distance when magnification is given.

Answer 1

The Correct Option is A

Step 1: Using the lens formula.
The lens formula is: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Where: - \( f \) is the focal length, - \( v \) is the image distance, - \( u \) is the object distance. Step 2: Relating the size of the image and object.
The magnification \( m \) of the lens is given by: \[ m = \frac{v}{u} \] Given that the magnification is \( n \) times the size of the object, we have: \[ n = \frac{v}{u} \] Step 3: Finding the image distance.
From the magnification equation, we can solve for \( v \): \[ v = n \cdot u \] Now substitute this into the lens formula: \[ \frac{1}{f} = \frac{1}{n \cdot u} - \frac{1}{u} \] Simplifying: \[ \frac{1}{f} = \frac{1-n}{n \cdot u} \] Thus, the image distance is: \[ v = F(n+1) \] Thus, the correct answer is (A) \( F(n+1) \).