Mirror Equation

Mirror equation is an experimental-based quantitative interrelationship between object distance, image distance, and focal length. The fundamental principles of the new Cartesian sign convention are used to understand the positions of the object, image, and mirror better. Concepts related to mirror equations and formulas are applied to spherical mirrors only. This article will help in understanding the concepts associated with the mirror equation. 

Concepts associated with mirror equation

The mirror equation represents an experimental-based quantitative interrelationship between object distance, image distance, and focal length. In other words, the mirror equation shows the direct relationship of image distance and object distance with the focal length of a circular mirror known as the mirror formula. 

The equation is represented as: 

1/v+1/u=1/f

In the case of spherical mirrors, including concave and convex mirrors, the following are the symbols that show different quantities: 

Object distance (u): The distance between the pole of the mirror and the object.

Image distance (v): The distance between the pole of the mirror and the image. 

Focal length (f): The distance between the pole of the mirror and the principal focus. 

In the field of ray optics, all three are interlinked with each other as per the equation represented below:

1/v + 1/u = 2/R = 1/f

In this,

u is the Object Distance

v is the Image Distance

f is the Focal Length 

The focal length and radius of curvature of the spherical mirrors represented by R are related to each other. The mirror formula is reliable and valid for all kinds of spherical mirrors (including convex and concave) and object positions. However, one needs to use sign symbols very carefully for calculating the distances. 

A new Cartesian sign convention is used for understanding ray directions and their signs and symbols. 

Following are the guidelines under this:

• The optical centre of the lens is used for measuring the distances. 
• The origin is the pole of the spherical mirror (p). 
• The x-axis is considered the principal axis of the coordinate plane. 
• The position of the object is always on the left side of the mirror, which indicates that light is on the left-hand side.
• When the direction of the incident light and distances are opposite, they are considered negative. 
• When the direction of the incident light and distances are the same, they are considered positive. 
• When the heights of the objects are upward and perpendicular to the principal axis, they are considered positive. 
• When the heights of the objects are downward and perpendicular to the principal axis, they are considered negative.

When a ray of light emerging out from an object is reflected and refracted to another point, the point is known as the image of the object. The formation of any image follows some fundamental guidelines and support pathways of rays and the exact location of the image. 

Some of the fundamental guidelines are mentioned below:

• When the light travelling is parallel to the principal axis, the reflected light passes through the focus of the mirror. 
• When the ray of light travels through the centre of the curvature, it reflects back and follows the original pathway.  
• When the ray of light travels through the focus of the mirror, then it passes parallel to the principal axis after reflection. 

In all the above cases, the angle of reflection is always equal to the angle of incident. 

Significance 

Mirror formulas help in identifying the exact location of the image formed of any object or image. Mirror equation is used in the field of ray optics for experimentation and understanding the nature, size, virtue, and effect of the image. This makes the process more simple and acceptable. However, one needs to be more careful while taking the readings of the object height, object distance, image height, and image distance to provide appropriate outcomes during the research and experiment.  

Conclusion

Thus, for identifying the object and image positions, the use of the mirror equation is very significant. Mirror equation is an experimental-based quantitative interrelationship between object distance, image distance, and focal length. The fundamental principles of the new Cartesian sign convention are used to understand the positions of the object, image, and mirror better. Concepts related to mirror equation and formula are applied to the spherical mirrors only.