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CBSE Class 10 Answered

derive the mirror formula with a ray diagram.
Asked by haritsourabhharit | 15 Oct, 2010, 01:05: PM
answered-by-expert Expert Answer
dear student

Mirror formula is the relationship between object distance (u), image distance (v) and focal length.

Derivation

The figure shows an object AB at a distance u from the pole of a concave mirror. The image A1B1 is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram.

Consider the D A1CB1 and D ACB

[when two angles of D A1CB1 and D ACB are equal then the third angle

But ED = AB

From equations (1) and (2)

If D is very close to P then EF = PF

But PC = R, PB = u, PB1 = v, PF = f

By sign convention

PC = -R, PB = -u, PF = -f and PB1 = -v

Equation (3) can be written as

Dividing equation (4) throughout by uvf we get

Equation (5) gives the mirror formula
 
We hope that clarifies your doubt
 
Regards
Team
TopperLearning
Answered by | 17 Oct, 2010, 10:07: AM

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