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Mirror Equation
A mirror equation is an equation relating object distance and image distance with focal length . It is also known as a mirror formula.
In a spherical mirror:
- The distance between the object and the pole of the mirror is called the object distance(u).
- The distance between the image and the pole of the mirror is called Image distance(v).
- The distance between the Principal focus and pole of the mirror is called Focal Length(f).
The above formula is valid under all situations for all types of spherical mirrors (Concave and Convex) and for all object positions.
Sign Conventions
New Cartesian Sign Convention is used to avoid confusion in understanding the ray directions. Refer to the diagram for clear visualization.
- For the measurement of all the distances, the optical center of the lens is considered.
- When the distances are measured opposite to the direction of the incident light, they are considered to be negative.
- When the distances are measured in the same direction of the incident light, they are considered to be positive.
- When the heights are measured upwards and perpendicular to the principal axis, they are considered to be positive.
- When the heights are measured downwards and perpendicular to the principal axis, they are considered to be negative.
Mirror Equation for concave mirror and Mirror Equation for a convex mirror
The mirror equation
1 v + 1 u = 1f
holds good for concave mirrors as well as convex mirrors.
Properties of a Concave Mirror
The properties of the concave mirror are:
- If the object is put in between the focus and mirror- In that case, the image form on the surface is virtual and bigger than the object and of the same orientation as the object.
- If the object is put in between the centre of the mirror and focus point- In this case, the image formation by the mirror is real and bigger than the object. In addition, the image formation is also inverted.
- The object is kept two focal distance away from the mirror- In that case, the image will be real and inverted. Besides, the image formation is smaller in size.
Image Formation By Concave Mirror
By changing the position of the object from the concave mirror, different types of images can be formed. Different types of images are formed when the object is placed:
- At the infinity
- Beyond the center of curvature
- At the center of curvature
- Between the center of curvature and principal focus
- At the principal focus
- Between the principal focus and pole
Use of Concave Mirror
The usage of a concave mirror is very common in many household devices and equipment like shaving mirrors, flashlight, headlight etc. and bigger devices such as aircraft, telescope etc.