# Mirror formula and the nature of the image formed by curved mirrors

Mirror formula and the nature of the image formed by curved mirrors

What is a Mirror formula for concave mirror? A mirror formula is a relationship between the object distance or height (u), image distance or height (v) and focal length of the mirror

Reflection of light by curved mirror

A concave mirror has a real principal focus; hence the focal length is positive.
It forms a real or visual image depending on the position of the object. Because it forms real image, the object distance and image distance from the mirror are both positive in mirror formula

. The mirror formula for concave mirror is given as

${ { \frac { 1 }{ f } =\frac { 1 }{ U } +\frac { 1 }{ V } } }$

Where f= focal length, u = object distance or height, and v=image distance or height

Mirror formula when the image distance is negative

${ { \frac { 1 }{ f } =\frac { 1 }{ U } -\frac { 1 }{ V } } }$

Mirror formula for convex mirror
Because the convex mirror does not form real image but virtual one , the image distance is negative, the focal length negative and object distance remains positive in convex  mirror formula and is given as
${ { \frac { 1 }{ u } -\frac { 1 }{ v } =\frac { -1 }{ f } } }$

The nature of image form by concave mirror

The nature and position of image formed by concave mirror for different position of an object could be determined using a ray box
The mirror is placed on a wooden stand and the light from the object is made to fall on centre of a concave mirror

The nature of Images are formed  when object is placed in front of concave mirror, depend on their position in the front of a concave mirror and therefore the nature of image forms by concave mirror are as follow

(i). When object is placed farther away from the mirror the image formed is real smaller than the object and inverted

(ii). When an object is place close to the mirror object get bigger real and inverted

(iii). When object is placed at the centre of curvature of the mirror the image is same size as the object, inverted and real

(iV).when object is placed between the centre of curvature and principal focus the image become larger than the object, real and inverted

(V). When an object is placed at the principal focus the image is no longer formed on the screen

(vi). when object is placed between the principal focus and the pole the image is larger, erect and ritual

Nature of image formed by convex mirror

The images formed by convex mirror are always erect, virtual, and smaller than the object no matter where the object is placed

Magnification in curved mirror

Magnification of object can be defined as how many times the image is bigger than object. It is given mathematically as:

${ { M=\frac { Image\quad Height }{ Object\quad Height } } }$

M=magnification

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