Sign convention for reflection by spherical mirrors Mirror formula and magnification

 

Sign convention for reflection by spherical mirrors



To deal with the reflection of light by spherical mirror, we have to follow a set of conventions is known as the new cartesian sign convention.

The pole of the spherical mirror is taken as the origin.

The principal axis of the spherical mirror is taken as the X-axis of the coordinate system.

The object is always placed to the left of the spherical mirror. It means to say that the ray of light coming from the object falls on the spherical mirror from the left handed side.

All the distances parallel to the principal axis are measured from the pole of the spherical mirror.

All the distances which are measured to the right (along +ve X-axis) are taken as the positive.

All the distance which are measured to the left of the origin (along -ve X-axis ) are taken as the negative.

The height measured perpendicular to the principal axis and are upward to the principal axis (along +ve Y-axis) are taken as positive.

The height  measured perpendicular to the principal axis and are downward to the principal axis (along -ve Y-axis) are taken as negative.

 

Sign convention for reflection by concave mirrors

The object is always placed to the left of the  mirror. It means to say that the ray of light coming from the object falls on the concave  mirror from the left handed side. Hence object distance is taken as negative.

The centre of curvature lies in front of the concave mirror, hence radius of the curvature are taken as negative in the case of the concave mirror.

The focus lies in front of the concave mirror, hence the focal length (f) are taken as negative in the case of the concave mirror.

When the image is formed , then All the distances which are measured to the right (along +ve X-axis) are taken as the positive.

When the image is formed , then All the distance which are measured to the left of the origin (along -ve X-axis ) are taken as the negative

If the image is above the principal axis , then the image height will be positive. It means  image is erect.

If the image is above the principal axis then the image height will be negative . it means the image is inverted.

 

Sign convention for reflection by convex mirrors

The object is always placed to the left of the mirror. It means to say that the ray of light coming from the object falls on the convex mirror from the left hand side. Hence object distance is taken as negative.

The centre of curvature lies behind the convex mirror , then the radius of the curvature are taken positive.

The focus of the convex mirror lies behind the convex mirror then the focal length of the convex mirror is taken as positive.

The image is always formed behind the mirror in the case of the convex mirror. Hence the distance of the image formed is taken as positive.

The image formed is always erect in the case of the convex mirror. Hence, the height of the image formed is taken as positive.

 

 

Mirror formula and magnification

 

Mirror formula states that there is a relationship between the object distance (u) , image distance (v) and the focal length (f). all distance are measured from the pole of the mirror.

Object distance (u) :--

                                 In the spherical mirror,  The distance of the object from its pole is called as object distance.

Image distance (v) :--    

                                In the spherical mirror, the distance of the image from its pole is called image distance.

Focal length (f) :--

                          The distance of the principal focus from the pole of the mirror is called the focal length.

 

The mirror formula is expressed as:--

 

1/v – 1/u  =  1/f

 

Magnification :--

                             Magnification produced  by the spherical mirror is expressed as the ratio of the height of the image to the height of the object.

Magnification is denoted by the letter (m).

Height of the object is h

Height of the image is h’

The magnification (m) produced by the spherical mirror is given by :--

                                         Height  of the image (h’)

Magnification (m) =      ........................................

                                         Height of the object (h)

 

            h’

M  =  …....

            h

The magnification (m) is also related to the object distance (u) and image distance (v).

This relationship is also expressed as :-

                                         h‘                           v

Magnification (m) =……………             =  -  ………

                                        h                             u

-ve (negative sign indicated that the image is real.

And the positive sign (+ve) indicated as the image is virtual.

Tabular form for different position of spherical mirror:--

Types of the mirror

Position of the object

Image distance

Focal length(f)

Height of the object

Magnification (m)

Height of the image

Concave mirror

Between  P&F

+ve

-ve

+ve

-ve

+ve

Concave mirror

Between F&c

-ve

-ve

+ve

-ve

-ve

Concave mirror

At C

-ve

-ve

-ve

-ve

-ve

Concave mirror

Beyond the C

-ve

-ve

+ve

-ve

-ve

Convex mirror

In font of it

+ve

+ve

+ve

-ve

+ve

 

 

 

 

 

 

 

 

 

 

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