The correct option is 1/v + 1/u = 1/f.
Explanation
In ray optics, the relationship between the position of the object, the position of the image, and the focal length of a spherical mirror is governed by the mirror equation. This relationship holds true for both concave and convex mirrors when the aperture of the mirror is small compared to its radius of curvature (paraxial approximation).
Analysis of the Formula:
- The correct mathematical representation of the mirror formula is:
1/v + 1/u = 1/f - Variables defined:
- u: Object distance (distance of the object from the pole of the mirror).
- v: Image distance (distance of the image from the pole of the mirror).
- f: Focal length (distance of the principal focus from the pole).
- Sign Convention: According to the Cartesian sign convention, distances measured in the direction of incident light are positive, while those measured against it are negative. The formula remains consistent regardless of the specific signs of u, v, or f in a given problem.
Comparison with Other Options:
- 1/v − 1/u = 1/f: The equation 1/v − 1/u = 1/f represents the lens formula, applicable to thin spherical lenses, not mirrors.
- Options v/u = f and v + u = f: These are mathematically incorrect representations of the relationship between these optical variables.
Key Takeaway:
The mirror formula involves the sum of the reciprocals of image and object distances (1/v + 1/u = 1/f), whereas the lens formula involves the difference (1/v − 1/u = 1/f).