the equations of spherical mirror derive equation for a straight mirror.prove that the magnification equal to 1.

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quantatanu | Student, Undergraduate | (Level 1) Valedictorian

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Equation of a spherical mirror is:

 

1/f = 1/d_i + 1/d_o

=> 2/r = 1/d_i + 1/d_o  ------------------------(1)

 

where, f = focal length = radius of the mirror (r)/2

d_o = object distance

d_i = image distance

 

Magnification (M)

= image height (h_i)/object height(h_o) = - d_i /d_o

A plane is a piece of a large sphere. So from this we can think of a plane mirror as a small piece of a giant spherical mirror, that is

 

Plane Mirror = Limit(r-->Infinity) [ Spherical Mirror]

so in equation (1) we see that 

2/Infinity = 1/d_i + 1/d_o

=> 0 = 1/d_i + 1/d_o

=> d_i = - d_o -----------------------(2)

Hence

Magnification(M) =  - d_i /d_o

Hence Magnification of a plane mirror

                            = - (-d_o)/d_o            [using (2) ]

                            = 1

Proved.

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