Using the lens maker's formula, derive the thin lens formula $\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$ for a biconvex lens.

Starting from refraction at the two surfaces (lens maker's result) and setting $u=\infty,\ v=f$ gives the lens formula $\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$.

CBSE Class 12 · 2020 · Geometrical OpticsShort Answer

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Using the lens maker's formula, derive the thin lens formula

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

for a biconvex lens.

Solution

Refraction through the two surfaces of a thin lens gives the general relation

\frac{1}{v} - \frac{1}{u} = (n - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}}) (i)

For an object at infinity (

u = \infty

) the image forms at the focus (

v = f

), so

\frac{1}{f} = (n - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}}) (ii) [lens maker’s formula]

Comparing (i) and (ii):

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

CBSE Class 12 Board · 2020 · Subjective

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