Question

A double convex lens has two surfaces of equal radii
'R and refractive index n = 1.5. find the focal
length
please I want step by step answer
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Answer 1

Answer:

R1 = R2 = R

n = 1.5

f = ?

By Lens maker's formula,

$\frac{1}{f} = (n - 1)( \frac{1}{r_{1} } + \frac{1}{ r_{2} } ) \: \: \: \: \: \\ = (1.5 - 1)( \frac{1}{r} + \frac{1}{r} ) \\ = 0.5( \frac{2}{r} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = \frac{1}{2} \times \frac{2}{r} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = \frac{1}{r } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = > \frac{1}{f } = \frac{1}{r} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > f = r \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

The focal length will be equal to the Radius of curvature of the biconvex lens.