Question

Which of the following indicates lens formula?

• A. $f = \frac{1}{v} - \frac{1}{u}$
• B. $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
• C. $\frac{1}{f} = v - u$
• D. $f = \frac{1}{v - u}$

Hint:

Always remember the lens formula in the form: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] It is one of the most frequently used formulas in ray optics.

Answer 1

The Correct Option is B

Concept: The lens formula is an important relation in geometrical optics that connects the focal length of a lens with the object distance and image distance. For a thin lens, the relationship between focal length ($f$), image distance ($v$), and object distance ($u$) is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Explanation: This formula is applicable for both convex and concave lenses when the proper sign convention is used. Where:
• $f$ = focal length of the lens
• $v$ = image distance from the optical center
• $u$ = object distance from the optical center The formula helps in determining:
• Position of image
• Nature of image
• Size of image
• Focal length of lens Among the given options, only option (2) correctly represents the standard lens formula.