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# Mirror Formula (Concave Mirror)

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

# Derivation of Lens Formula (Concave Lens)

Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. The image A1B1 is formed between O and F1 on the same side as the object is kept and the image is erect and virtual.

OF1 = Focal length = f

OA = Object distance = u

OA1 = Image distance = v

But from the ray diagram we see that OC = AB

From equation (1) and equation (2), we get

Dividing throughout by uvf

# Derivation of Lens Formula (Convex Lens)

Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. The image A1B1 is formed beyond 2F2 and is real and inverted.

OA = Object distance = u

OA1 = Image distance = v

OF2 = Focal length = f

OAB and OA1B1 are similar

But we know that OC = AB

the above equation can be written as

From equation (1) and (2), we get

Dividing equation (3) throughout by uvf

HOPE THIS HELPS U.........

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