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Convex Mirror: Uses, Equation, Difference Between Concave and Convex Mirror

When a hollow spherical is split into pieces and the exterior surface of each cut portion is painted, it forms a mirror, with the internal layer reflecting the light. The reflecting surface formed is called a concave mirror.

Concave Mirror

Concave mirrors reflect rays of light and develop images by these reflected rays of light. Concave mirrors can produce both real and virtual images, depending on the object’s location.

Convex Mirror

A convex mirror is depicted in the diagram below. A convex mirror is a sphere that has had a piece of it cut away. The mirror is termed to be convex if the outside of the sphere is silvered and can reflect light. This line that runs from the mirror's base to the sphere's center is the main axis. The initial sphere's center of curvature (C) is considered the center of curvature c. The focal point (F) of the mirror is placed halfway between the mirror's surface and the center of curvature along the primary axis.

The point in space where light appears to diverge from is called an image. As a result of reflected light, any observer from any position viewing along a line at the image location will see the object. Regardless of the observer's location, each observer sees the image in the same place. A ray of light reflects off the mirror and into the observer's eye as the observer looks along a line. As a result, locating where reflected light intersects is the challenge The illustration below depicts an object in front of a convex mirror.

The accompanying illustration is an imaginary depiction of image formation in a convex mirror. The image’s location prevents light from passing through it. Observers only see the light reflected from each component of the object departing from this imaginary image location. Since all the items reflecting light seem to diverge from this location in time, anybody looking across a line at this location will see a duplicate or replica.

Each incidence angle that travels parallel to the primary axis will reflect so that its expansion travels via the focal point. Any incident ray traveling to a convex mirror via the focal point will rebound and move parallel to the primary axis.

Mirror Equation

It gives the relation between object distance and image distance with focal length.
In a spherical mirror,
Distance between the object and the pole of the mirror is object distance(u).
Distance between the image and the pole of the mirror is Image distance(v).
Distance between the principal focus and pole of the mirror is Focal Length(f).

The object distance, image distance, and Focal length make up the mirror equation given below,

1 / v + 1 / u = 1 / f

Where,
u is the object distance
v is the image distance
And f is the focal length
Also, f = R / 2
R is the radius of curvature of the spherical mirror
This formula holds true for both convex and concave mirrors and for all object positions.

New Cartesian Sign Convention

When a distance is measured opposite to the direction of the incident light, it is taken to be negative.
When a distance is measured in the same direction of the incident light, it is taken to be positive.
When a height is measured upwards and perpendicular to the principal axis, it is taken to be positive.
When a height is measured downwards and perpendicular to the principal axis, it is taken to be negative.

Uses of Convex Mirror

  • Convex mirrors are used in hallways of buildings to provide a larger field of view.
  • They are used on roads to provide safety to bikers and motorists at curves, turns, and other blind spots.
  • They are also used in automated teller machines as a security feature that allows users to see what is happening behind them.
  • They are used on the passenger side mirror of a car and are labeled “objects in the mirror are closer than they appear” to warn the driver about approaching vehicles.

 

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