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

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### 1 Answer

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.**