Correct Option: (C) $\sqrt{X_1 X_2}$
Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]
According to Newton’s form of the lens equation, for a lens with focal length $f$, if the distance of the object from the first focal point is $X_1$ and the distance of the image from the second focal point is $X_2$, the relationship is given by:
$$X_1 X_2 = f^2$$Where $X_1$ and $X_2$ are the distances measured from the respective focal points.
Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]
To find the focal length $f$, we take the square root of both sides of the equation derived from the lens formula:
$$f^2 = X_1 X_2$$ $$f = \sqrt{X_1 X_2}$$Step 3 (Final Concluded Answer): [0.25 Mark]
The focal length of the lens is $\sqrt{X_1 X_2}$. Thus, the correct option is (C).
💡 EL10 Concept Insight:
Think of this as a "geometric mean" relationship; because the lens bends light symmetrically around its focal points, the focal length acts as the perfect balance point between the object's distance from one focus and the image's distance from the other.