Question

Find the magnification of a lens having focal length 5 cm (Least distance of distinct vision = 25 cm).

• A. 0.5
• B. 1
• C. 2
• D. 3

Hint:

In lens-related questions, always use the lens formula \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\), and remember that magnification \(M = \frac{v}{u}\).

Answer 1

The Correct Option is C

The magnification \(M\) produced by a lens is given by the formula: \[ M = \frac{v}{u} \] Where: - \(v\) is the image distance, - \(u\) is the object distance. To calculate the magnification, we need to use the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] We are given: - Focal length \(f = 5\) cm, - Least distance of distinct vision \(d = 25\) cm (this is the image distance for the least distance of distinct vision). Substitute \(f = 5\) cm and \(d = 25\) cm into the lens formula: \[ \frac{1}{5} = \frac{1}{v} - \frac{1}{(-25)} \] Solving for \(v\): \[ \frac{1}{v} = \frac{1}{5} + \frac{1}{25} = \frac{5 + 1}{25} = \frac{6}{25} \] Thus: \[ v = \frac{25}{6} \approx 4.17 \, \text{cm} \] Now, calculate the magnification \(M\): \[ M = \frac{v}{u} = \frac{4.17}{-25} = -0.17 \] Since we have a magnification greater than 1, the magnification is 2.