What is a Mirror?
The law of reflection states that when a ray of light is made to fall on the reflecting surface, the incident ray, the reflected ray, and the normal to the surface of the mirror all lie in the same plane and the angle of incidence is equal to the angle of reflection.
Types of Mirrors
The following are the most common types of mirrors:
Plane mirror:
The reflected images in their normal proportions but reversed from left to right are formed by a plane mirror.
These are curved outward spherical mirrors, and the image obtained is virtual, diminished, and erect for a real object.
Concave mirrors:
These are curved inward spherical mirrors, and the image obtained from these mirrors is dependent on the placement of the object.
What is Mirror Formula?
The mirror formula is the relationship between the focal length of the mirror, the object's distance u from the pole of the mirror, and the image's distance v from the pole.
The mirror equation is
1/v +1/u = 1/f.
Mirror Formula Explanation
The Mirror formula represents the relationship between the object distance (u), image distance (v), and focal length (f) of a Spherical Mirror. The mirror equation is written as follows:
1/f = 1/v+1/u
Here, u and v represent the distances of the object and image from the mirror's pole, respectively. And Focal Length (f) is the distance between the primary focus and the pole.
Using the equation below, we can calculate the magnification (m) of the object using u and v.
m=−v/u
The radius of curvature (R) is twice its focal length.
R=2f
and f=R/2
Hence, the Mirror equation can be written as:
1/u+1/v = 1/f= 2/R
Sign Conventions
The new Cartesian Sign Convention is used to avoid confusion in understanding the ray directions. Refer to the diagram for a better understanding.
- The optical center of the lens is taken into account when measuring all distances.
- Distances are considered negative when measured in the opposite direction of the incident light.
- Distances are considered positive when measured in the same direction as the incident light.
- Height is considered positive when measured upwards and perpendicular to the principal axis.
- Height is considered negative when measured downwards and perpendicular to the principal axis.
Read More About: Mirror Formula Derivation
Applications of Mirror Equation
The Mirror Equation is used in the following ways:
When the object distance and the focal length of the mirror are known, the mirror equation can be used to predict the image distance.
When we know the image distance and the focal length of the mirror, we can use the equation to calculate the object distance.
The mirror equation allows us to calculate the focal length of the mirror simply by knowing the distance between the object and the image it forms.
When we use the mirror equation in conjunction with the magnification equation, we can obtain the value of either the image height or the object height when the other is given.
Things to remember
- Optics is the branch of physics that deals with light, its behavior patterns, and qualities.
- Light is a type of electromagnetic radiation that enables the human eye to see or renders objects visible. It is also known as radiation that can be seen with the naked eye.
- The focal length of a lens determines its ability to converge or diverge light rays.
- We can use mirror formulas and equations to determine where the image will be produced if we know the object position and the focal length of the mirror.
- A mathematical formula that connects the object distance, image distance, and mirror focal length is known as the Mirror Formula.
- The mirror formula is 1/f = 1/v + 1/u
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Solved Examples
Q1. Calculate magnification of concave mirror if the image of an object formed in front of a concave mirror with a focal length of 12 cm is formed at a point 10 cm away from the mirror.:
Solution
The magnification of the image is:
Q2. The radius of curvature of a convex mirror used for rearview on a bus is 4m. Determine the position of the image if a car is 2m away from the mirror.
Solution:
