Question

If \(m_1\) and \(m_2\) (\(m_1 \geq m_2\)) are the magnification for two positions of the lens between the object and the screen, and \(d\) is the distance between the two positions of the lens, the focal length of the lens is:

• A. \(\frac{m_1 - m_2}{d}\)
• B. \(\frac{m_1 m_2}{d}\)
• C. \((m_1 - m_2)d\)
• D. \(\frac{d}{m_1 - m_2}\)

Hint:

When analyzing lens movement and magnification, understanding the relationship between object and image distances simplifies the calculation of focal lengths.

Answer 1

The Correct Option is D

Step 1: Analyze the magnification formula. \[ m = -\frac{v}{u} \] where \(v\) is the image distance and \(u\) is the object distance. 
Step 2: Apply the lens formula for different positions. Using the lens formula, \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\), and the changes in magnification, \[ f = \frac{d}{m_1 - m_2} \]