Question

(ii) A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.

Hint:

The magnification of a lens is given by the ratio of the image distance to the object distance. The lens formula helps to relate object distance, image distance, and focal length.

Answer 1

Given: - The magnification (\(M\)) is -3 (since the image is inverted).
- The object distance (\(u\)) is -15 cm (negative because the object is on the left of the lens).
We can use the magnification formula and the lens formula to calculate the focal length of the lens.
1. Magnification Formula:
The magnification (\(M\)) is given by the formula: \[ M = \frac{v}{u} \] Where: - \(v\) is the image distance (positive for real images, negative for virtual images),
- \(u\) is the object distance (always negative in lens formulas for objects to the left of the lens).
We know that the magnification is -3, so: \[ -3 = \frac{v}{-15} \] Solving for \(v\): \[ v = 45 \, \text{cm} \] 2. Lens Formula:
The lens formula relates the focal length (\(f\)), object distance (\(u\)), and image distance (\(v\)): \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Substituting the known values of \(v = 45 \, \text{cm}\) and \(u = -15 \, \text{cm}\): \[ \frac{1}{f} = \frac{1}{45} - \frac{1}{-15} = \frac{1}{45} + \frac{1}{15} \] Simplifying: \[ \frac{1}{f} = \frac{1 + 3}{45} = \frac{4}{45} \] Therefore, \[ f = \frac{45}{4} = 11.25 \, \text{cm} \] Conclusion:
The focal length of the convex lens is \(11.25 \, \text{cm}\).