Derive the Mirror Formula PDF

Today we will learn how to derive the mirror formula. In the board examinations, you are asked to derive the mirror formula.

What is the mirror formula?

The mirror formula is the relation among object distance(u), image distance(v), and focal length (f) of the spherical mirror.

To derive the mirror formula, we will use a concave mirror.

Derivation of mirror formula

Let the object AB of size or height(h) is placed on the left in front of the concave mirror MN beyond its centre of curvature C.

Using the New Cartesian Sign Convention, and the aperture of the mirror is assumed to be very small, then O is near P.

Object distance = OB=PB=-u

Image distance = `OB^'=PB^'=-v`

Radius of curvature= QC=PC=  -R

                                              =  -2f

In right-angled similar triangles  `A^' B^' F`  and MPF

`frac{A'B'}{MP}=frac{B'F}{PF}`

Or

  

`frac{A'B'}{AB}=frac{(u-f)}{f}`    ………….(i) [MP=AB]

In right-angled similar triangles ABC and A’B’C

`frac{A'B'}{AB}=frac{B'C}{BC}=  frac{2f-v}{u-2f}`   …………….(ii)

Now compare the equations (i) and (ii)

`frac{v-f}{f}=frac{2f-v}{u-2f}`

 

`uv-uf-2vf+2f^2=2f^2-vf`  

`⟹    uv=vf+uf`

Dividing both sides by uvf

`frac{uv]{uvf}=frac{vf}{uvf}+ frac{uf}{uvf}` 

`frac{1}{f}=frac{1}{u}+frac{1}{v}`   

Now you can learn how to derive the mirror formula. This mirror formula is used in solving numerical questions. This topic is useful for both class 10 and 12 students.

FAQ

   1. What is the mirror formula class 10, explain?

Ans - The mirror formula is the relation among object distance(u), image distance(v), and focal length (f) of the spherical mirror.

 

   2. What is magnification?

Ans- The ratio between the size of an image and the size of the object is called magnification. It is denoted by ‘m’.

  

   3. Is the mirror formula important for class 12?

Ans.  The mirror formula is important for class 12, numercal questions are asked on this formula.

4. Is the mirror formula applicable to the plane mirror?

Ans- The mirror formula is applicable for plane mirror and spherical mirrors, as we all know that mirrors are cut from the spherical mirror when cut in different parts, the  middle part become plane and the other two is convex and concave. So we can easily understand that the mirror formula is applicable to the plane mirrors also.

 

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