Mirrors 

A mirror is a smooth surface often made of glass with a reflective coating, usually either silver or aluminium, where the light is reflected to form an image. Mirrors are used frequently in many applications such as personal grooming, telescopes, cameras, and a part of scientific instruments.

1.0Types of Mirror 

Mirrors are divided into three types based on their shapes: 

• Plane Mirrors
• Concave Mirrors 
• Convex Mirrors

Concave and Convex are collectively called Spherical mirrors, which are curved mirrors on either side and affect their properties. 

Plane Mirrors

Plane Mirrors have a flat reflective surface. It creates an image that is: 

• The image formed by any plane mirror is virtual; that is, it can not be projected on the screen. 
• The image created is always upright and in the same orientation as the object. 
• The image produced is of the same size as the object.
• The image created is laterally inverted, meaning the left and right sides of the image are reversed.
• The image produced is of equal distance of the object from the mirror. 
• The image formed is always behind the mirror. 

Uses of Plane Mirrors

• Plane Mirrors are used for personal grooming in the bathrooms and dressing rooms. 
• Plane mirrors can also be used for decorative purposes like in homes, offices, and vehicles. 

Spherical Mirrors 

Spherical mirrors are the type of mirrors whose reflecting surface forms part of a sphere. These can further be divided into two types:

1. Concave Mirrors (Converging mirrors)
2. Convex Mirrors (Diverging mirrors)

Concepts Related to Spherical Mirrors

1. Center of Curvature(C): It is the centre of that sphere from where the spherical mirror is taken. 

2. Principle Axis(P): It is the imaginary line through the centre of curvature and midpoint of the reflecting surface(a’b’ or ab) of the mirror. 

3. Focus: Focus is the point in the midpoint between the centre of curvature and the Principle axis. The distance between points F and P is known as the Focal length. 

Concave Mirror (Converging Mirrors) 

A concave mirror has an inwardly curved reflecting surface. This allows converging light rays to the focal point. The concave mirror forms real or virtual images; they are either erect or inverted.

Position of object	Figure	Position of image	Nature of image
Infinity		At Focus	Real, inverted, and highly Diminished
Beyond C		Between C and F	Real, inverted, and Diminished
At C		At C	Real, inverted, and same size
Between C and F		Beyond C	Real, inverted, and bigger than the object
At F		At Infinity	Real, inverted, and extremely big
Between F and P		In front of the mirror	Virtual, erect, and magnified

Convex Mirror

A convex mirror has an outward-curved surface. Rays diverge from the incoming rays and seem to appear to emanate from one point behind the mirror.

Position of Object	Diagram	Position of Image	Nature of Image
At Infinity		At Focus	Virtual, erect, and highly diminished
Anywhere in front of the mirror		Between P and F	Virtual, erect, and diminished

2.0Mirror Formula for Spherical Mirrors

The mirror formula for Spherical mirrors gives the following relationship between the focal length (f), object distance (u), and the image distance (v):

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

According to the sign convention: 

• f is the focal length, which is positive for convex mirrors and negative for concave mirrors.
• v is the image distance for real images and the negative image distance for virtual images.
• u is the object distance (always negative as per sign conventions).

3.0Spherical Mirror Questions 

Problem 1: A concave mirror has a focal length of 15 cm. An object is placed 30 cm in front of the mirror. Find the position, size, and nature of the image formed.

Solution: f = –15cm, u = –30cm 

Using the mirror formula 

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{-15}=\frac{1}{v}+\frac{1}{-30}$

$\frac{1}{v}=\frac{1}{15}-\frac{1}{30}$

$-\frac{1}{v}=\frac{2-1}{30}=\frac{1}{30}$

v=-30cm

Hence, the image is real and inverted, placed on the centre of curvature, and of the same size.

Problem: A convex mirror has a focal length of 20 cm. An object is placed 40 cm in front of the mirror. Find the position and nature of the image.

Solution: f = 20cm, u = –40cm 

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{20}=\frac{1}{v}+\frac{1}{-40}$

$-\frac{1}{v}=\frac{1}{-20}-\frac{1}{40}$

$-\frac{1}{v}=\frac{-2-1}{40}$

$-\frac{1}{v}=-\frac{3}{40}$

v=40/3 cm

Hence the image will be formed behind the mirror and is virtual and erect. 

Problem: A spherical mirror has a focal length of 12 cm. An object is placed 36 cm in front of the mirror, and the size of the image is bigger than the object. Find the position and nature of the image. 

Solution: Given that the image of the spherical mirror is bigger than the object hence the spherical is the concave mirror. So, 

f = -12 cm, u = –36cm 

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{-12}=\frac{1}{v}+\frac{1}{-36}$

$-\frac{1}{v}=\frac{1}{12}-\frac{1}{36}$

$-\frac{1}{v}=\frac{3-1}{36}=\frac{2}{36}=\frac{1}{18}$

v=-18cm

The position of the image is in front of the mirror, and it is real and inverted.