Question

An object stands 4 cm in front of a converging lens. If the lens has a focal distance of 1 cm, where is the image formed?

• A. 0.75 cm in front of the lens
• B. 0.75 cm behind the lens
• C. 1 cm behind the lens
• D. 1.33 cm behind the lens

Hint:

For converging lenses, the image formed is real and located behind the lens when the object is placed at a distance greater than the focal length.

Answer 1

The Correct Option is D

The lens formula is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where \( f \) is the focal length, \( v \) is the image distance, and \( u \) is the object distance.
Given that the object distance is \( u = -4 \, \text{cm} \) (negative because it is in front of the lens) and the focal length is \( f = 1 \, \text{cm} \), we can rearrange the lens formula to solve for \( v \): \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{1} + \frac{1}{-4} = 1 - 0.25 = 0.75 \] \[ v = \frac{1}{0.75} = 1.33 \, \text{cm} \]
Thus, the correct answer is (d).