Optical Lens Formula

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This gives the relation between focal length, object distance and image distance from the optical centre of the lens.

Convex Lens (Real Image)

formation of image on convex lens

Consider an object AB held perpendicular to the principal axis at distance beyond the focal length of the lens. A real, inverted and enlarged image is formed as shown.

But CD=AB

It follows

BC = -u

BlC = +v using sign convention

CF = +f

FBl = CBl - CF = v - f

vf = -uv + ufuv = uf - vf

Dividing throughout by uvf

relation between focal length object distance image distance

Note:

(1) The above formula is applicable for a convex lens when a virtual image is formed. For this the following ray diagram is to be considered.

ray diagram of convex lens forming virtual image

2) For concave lens, the ray diagram would be

ray diagram of concave lens forming virtual image

Linear Magnification Produced by a Lens

linear magnification of lens

Convex Lens

Real Image

linear magnification of convex lens forming real image

Virtual Image

linear magnification convex lens virtual image

Concave Lens

linear magnification concave lens real image

linear magnification concave lens virtual image



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