How was mirror formula derived ?

Asked by saif abbas | 21st Nov, 2010, 12:19: PM

Expert Answer:

Dear student

A formula giving the relation between focal length of the mirror, object distance, image distance and radius of curvature.

 

 

 

Depending on the position of the object, the image formed may be real or virtual.

 

When the object is placed beyond 'C', the image is formed between 'C' and 'F'. Since the reflected rays actually meet at A', the image is said to be real.

 

 

 

 

 

from the above two equations we have

 

 

Since all distances are measured from P

 

CB = PB - PC

 

CBl = PC - PBl

 

Therefore,

 

 

Using the sign convention,

 

PB = - u (object distance)

 

PC = -R

 

PB = -v (Image distance)

 

On substitution,

 

+uR - uv = uv - vR

 

uR + vR = 2uv

 

Dividing both sides by uvR, we have

 

 

 

where f is the focal length of the mirror.

 

Note:

The above mirror formula is same for convex mirror for which image is always virtual.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

We hope this clarifies your doubt.

Regards

Team

Topperlearning

Answered by  | 21st Nov, 2010, 02:40: PM

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