Question

The distance of an object from the first focal point of a biconvex lens is \( X_1 \) and distance of the image from second focal point is \( X_2 \). The focal length of the lens is:

• A. \( X_1 X_2 \)
• B. \( \sqrt{X_1 + X_2} \)
• C. \( \sqrt{X_1 X_2} \)
• D. \( \frac{X_2}{X_1} \)

Hint:

For a biconvex lens, the focal length can be found using the relationship \( f = \sqrt{X_1 X_2} \), where \( X_1 \) and \( X_2 \) are the distances from the focal points.

Answer 1

The Correct Option is C

For a biconvex lens, the relationship between the object and image distances and the focal length \( f \) is given by: \[ \frac{1}{f} = \frac{1}{X_1} + \frac{1}{X_2} \] However, in this case, since the object is placed at a distance \( X_1 \) from the first focal point and the image is formed at a distance \( X_2 \) from the second focal point, the correct formula for the focal length is derived from their product: \[ f = \sqrt{X_1 X_2} \] Thus, the focal length of the lens is \( \sqrt{X_1 X_2} \).