Mirror Equation in Physics

Mirror Equation

• The mirror equation relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror:
  • 1/u + 1/v = 1/f
• The equation is valid for both concave and convex mirrors
• Sign conventions:
  • Object distance (u) is negative for real objects and positive for virtual objects
  • Image distance (v) is positive for real images and negative for virtual images
  • Focal length (f) is negative for concave mirrors and positive for convex mirrors

Nature Of Image

• The nature of the image formed by a spherical mirror depends on the type of mirror and the object's position:
  • Real image: formed by a concave mirror when the object is beyond the focal length
  • Virtual image: formed by a convex mirror or when the object is within the focal length of a concave mirror
  • Inverted image: formed by a concave mirror when the object is beyond the focal length
  • Upright image: formed by a convex mirror or when the object is within the focal length of a concave mirror

Image Formation

• Image formation by a spherical mirror involves the following steps:
  1. Incident rays from the object strike the mirror
  2. Reflected rays converge or diverge to form the image
  3. The image is formed at the point where the reflected rays intersect
• The process of image formation can be explained using the concept of virtual rays and the law of reflection

Magnification

• Magnification (m) of an image formed by a spherical mirror is given by:
  • m = -v/u
• The magnification is negative for real and inverted images, and positive for virtual and upright images
• The absolute value of magnification represents the size of the image relative to the object:
  • |m| > 1: image is magnified
  • |m| < 1: image is diminished
  • |m| = 1: image is the same size as the object

Mirror Equation

• The mirror equation is 1/u + 1/v = 1/f, relating object distance (u), image distance (v), and focal length (f) of a spherical mirror.
• The equation is valid for both concave and convex mirrors.

Sign Conventions

• Object distance (u) is negative for real objects and positive for virtual objects.
• Image distance (v) is positive for real images and negative for virtual images.
• Focal length (f) is negative for concave mirrors and positive for convex mirrors.

Image Nature

• A real image is formed by a concave mirror when the object is beyond the focal length.
• A virtual image is formed by a convex mirror or when the object is within the focal length of a concave mirror.
• An inverted image is formed by a concave mirror when the object is beyond the focal length.
• An upright image is formed by a convex mirror or when the object is within the focal length of a concave mirror.

Image Formation

• Incident rays from the object strike the mirror.
• Reflected rays converge or diverge to form the image.
• The image is formed at the point where the reflected rays intersect.
• Image formation involves virtual rays and the law of reflection.

Magnification

• Magnification (m) is given by m = -v/u.
• Magnification is negative for real and inverted images, and positive for virtual and upright images.
• |m| > 1: image is magnified.
• |m| < 1: image is diminished.
• |m| = 1: image is the same size as the object.

Reflection of Light by Spherical Mirrors

Magnification

• Magnification is the ratio of the height of the image to the height of the object, denoted by m.
• The formula for magnification is m = -di/do, where di is the distance of the image from the mirror and do is the distance of the object from the mirror.
• Magnification is negative for real images and positive for virtual images.

Image Formation

• Image formation by spherical mirrors follows the principle of reversibility of light.
• The image formed by a spherical mirror can be real or virtual, depending on the position of the object.
• Real images are formed in front of the mirror, while virtual images are formed behind the mirror.

Mirror Equation

• The mirror equation is 1/f = 1/do + 1/di, where f is the focal length of the mirror.
• This equation is used to calculate the distance of the image from the mirror, given the distance of the object and the focal length.
• The mirror equation is applicable to both concave and convex mirrors.

Nature of Image

• The nature of the image formed by a spherical mirror depends on the position of the object.
• The image can be real and inverted, real and upright, virtual and inverted, or virtual and upright.
• The nature of the image can be determined by the sign of the magnification and the distance of the image from the mirror.

Sign Conventions

• The New Cartesian sign convention is used to describe the reflection of light by spherical mirrors.
• In this convention, distances of the object and image are measured from the pole of the mirror.
• Distances to the right of the mirror are positive, while distances to the left are negative.
• Heights of the object and image above the principal axis are positive, while heights below the principal axis are negative.