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Starting with an expression for refracti...

Starting with an expression for refraction at a single spherical surface, obtain Lens Maker.s formula.

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Let a convex lens is taken which is made up of glass of refractive index `n_(2)`. Let .O. is the point object placed on the principal axis and .u. is the distance of the object from `P_(1)`.

For refraction at the first surface
`(n_(2))/(v.)-(n_(1))/(u)=(n_(2)-n_(1))/(R_(1))" "......(1)`
For refraction at the second surface
`(n_(1))/(v)-(n_(2))/(v.-t)=(n_(1)-n_(2))/(R_(2))`
If the lens is thin `tltltltv.`, so
`(n_(1))/(v)-(n_(1))/(u)=(n_(2)-n_(1))((1)/(R_(1))-(1)/(R_(2)))`
Dividing both sides by `n_(1)`, we get
`(1)/(v)-(1)/(u)=((n_(2))/(n_(1))-1)((1)/(R_(1))-(1)/(R_(2)))`
Putting `(n_(2))/(n_(1))=n`, we get
`(1)/(v)-(1)/(u)=(n-1)((1)/(R_(1))-(1)/(R_(2)))`
When object is at infinity, image will be at focus
So, `(1)/(f)-(1)/(oo)=(n-1)((1)/(R_(1))-(1)/(R_(2)))`
`(1)/(f)=(n-1)((1)/(R_(1))-(1)/(R_(2)))`
This is lens maker.s formula
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