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Image Formation In Convex Mirror

Image Formation In Convex Mirror

A convex mirror is a type of spherical mirror where the reflecting surface is curved outward, away from the centre of the sphere. The surface of the mirror bulges out, facing the light source. Convex mirrors always form virtual, erect, and diminished images of objects placed in front of them. These mirrors are called diverging mirrors because they cause parallel light rays incident on their surface to diverge.

Image formation

  Convex Mirror

Some Important Terminology

    formula

Image Formation by Ray Diagram

Two positions of the object are considered for image formation. First is when the object is at infinity, and second is when the object is between infinity and the pole. The ray diagrams for the image formation by a convex mirror are shown below :

 

Object At Infinity :

When an object is placed at infinity, rays parallel to principal axis reflect off the mirror, which appears to converge at an imaginary point (focus) behind the mirror. It is created by extending the reflected rays backwards. The image formed is a virtual image, diminished, upright, and behind the mirror. 

 

Image formation

Object at Infinity

Object Between Infinity and Pole :

When an object is placed between infinity and the pole, the image is formed using two rays. One ray is parallel to the principal axis, which is extended backwards, and the other is directed towards the centre of curvature of the mirror. These rays intersect to form an image between the pole (P) and focus (F) behind the mirror. This image is virtual, smaller, upright, and appears behind the mirror.

 Object Between Infinity and Pole

Object Between Infinity and Pole

Mirror Formula -

formula

where,

f (focal length) - distance of the principal focus from pole

v - distance of the image from pole

u - distance of the object from pole

For convex mirror, focal length (f) and image distance (v) are considered positive, while the object distance (u) is taken as negative according to the sign convention.

Magnification Formula -

formula

where,

m (magnification)

h′ - height of image

h - height of object

Magnification is positive but less than 1 due to virtual and smaller image.

It can also be expressed as -

formula

A positive sign in the value of the magnification represents that the image is virtual.

Application of Convex Mirror

  1. Rear-view mirrors in vehicles
  2. Traffic and blind spot at roadside
  3. Security mirrors in shops and stores
  4. ATMs and elevators

Summing Up

A convex mirror is a diverging mirror with an outward-curved reflecting surface. It always forms a virtual, erect, and diminished image. The image appears to form behind the mirror. Light rays diverge after reflection, but when extended backward, they appear to meet at a point behind the mirror.

Position of the Object Position of the Image Size of the Image Nature of the Image
At infinity At the focus (F), behind the mirror Highly diminished Virtual and erect
Between infinity and pole (P) of the mirror Between pole (P) and focus (F), behind the mirror Diminished Virtual and erect

Frequently Asked Questions

Q1. Does the nature of the image change with the position of the object?

No. In a convex mirror, the image remains virtual, erect, and diminished, regardless of the position of the object.

Q2. Why are convex mirrors used as rear-view mirrors in vehicles?

They have a wider field of view as they are curved outwards. It enables the driver to view much larger area.

Q3. What does it indicate when magnification is positive and less than 1?

It represents that the image formed is virtual, erect, and very small.

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