Question

Derivation of Lens Formula?

Answer 1

Explanation:

Derivation of Lens Formula Consider a convex lens with an optical center O. Let F be the principle focus and f be the focal length. An object AB is held perpendicular to the principal axis at a distance beyond the focal length of the lens. A real, inverted magnified image A'B' is formed

Answer 2

Answer:

The figure above shows that the formation of a real, inverted and diminished image AB of the object AB placed beyond the centre of curvature at a distance u from the convex lens. Let v be the image distance,

According to Cartesian sign convention

Object distance (OB)=−u

Image distance (OB)=+v

Focal length (OF1=OF2)=+f

From the geometry of the figure above, right angled △ ABO and △ ABO are similar.

∴A′B′AB=O′B′OB=−v ........ (i)

Similarly, from the geometry of the figure above, right angled △ODF2 and △BAF2 are similar.

∴A′B′OD=F2B2OF2

∴A′B′AB=F2B2OF2 ( ∵ OD = AB, are the opposite sides of □ ABOD )

∴A′B′AB=OB′−OF2OF2

∴

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