What is the v in mirror formula?

The 'v' in the mirror formula represents the image distance, which is the distance between the image formed by the mirror and the pole (center) of the mirror.

Understanding Image Distance (v) in Detail

The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror:

1/f = 1/v + 1/u

Where:

• f = focal length of the mirror (distance from the pole to the focal point)
• v = image distance (distance from the pole to the image)
• u = object distance (distance from the pole to the object)

Key Points about 'v':

• Sign Convention is Crucial: The sign of 'v' is important. By convention:

  • For real images (formed by actual intersection of light rays), 'v' is positive. Real images are formed on the same side as the incident light rays (usually in front of the mirror for concave mirrors).
  • For virtual images (formed by the apparent intersection of light rays), 'v' is negative. Virtual images are formed behind the mirror.

• Determining Image Characteristics: The value of 'v' helps determine the location and nature of the image:

  • A large positive 'v' indicates a real image formed far from the mirror.
  • A small positive 'v' indicates a real image formed close to the mirror.
  • A negative 'v' indicates a virtual image formed behind the mirror. The magnitude of 'v' indicates how far behind the mirror the image is.

• Examples:

  • Consider a concave mirror. If an object is placed beyond the center of curvature (2f), a real, inverted, and diminished image is formed between the focal point (f) and the center of curvature (2f). In this case, 'v' would be positive and less than 2f.

  • If an object is placed between the pole and the focal point of a concave mirror, a virtual, erect, and magnified image is formed behind the mirror. In this case, 'v' would be negative.

Importance of 'v' in Calculations

Knowing the value of 'v', along with 'u' and 'f', allows for the determination of other important image characteristics, such as magnification. Magnification (m) is defined as the ratio of the image height (h') to the object height (h):

m = h'/h = -v/u

Therefore, the image distance 'v' is a fundamental parameter in understanding and analyzing image formation by mirrors.