Question

derive lens maker formula for convex lens​

Answer 1

Explanation:

Consider a thin convex lens made of a material of absolute refractive index n2 , placed in a rarer medium of absolute refractive index n1.

Also, n = n2 / n1 be the refractive index of the material of the lens with respect to the medium surrounding it.

R1 and R2 are the radii of curvature of surfaces XP1Y and XP2Y respectively.

For refraction at surface XP1Y : O is the object and I1 is its real image.

Using the formula, n2 / v – n1 / u = n2 – n1 / R1

we get, n2 / v1 – n1 / u = n2 – n1 / R1 -------------------Eqn (1)

For refraction at surface XP2Y : I1 is the virtual object and I is its real image which is the final image.

Using the formula, n1 / v – n2 / u = n1 – n2 / R1

we get, n1 / v – n2 / v1 = n1 – n2 / R2 -------------------Eqn (2)

Adding equations (1) and (2), we get n1 (1/v – 1/u) = (n2 – n1)(1/R1 – 1/R2)

Divide both sides by n1 we get, (1/v – 1/u) = (n2 – n1)/n1 (1/R1 – 1/R2)

1/f = (1/v – 1/u) = (n2/n1 – 1) (1/R1 – 1/R2)

1/f = (1/v – 1/u) = (n – 1) (1/R1 – 1/R2)

This is called lens maker s formula.

Hope it helps you

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