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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.........

THUMBS UP! IF U R SATISFIED.........

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