A thin convex lens made from crown glass has focal length f. When it is measured in two different liquids having refractive indices , it has the focal lengths f1 and f2 respectively. The correct relation between the focal lengths is :

Engineering

Physics

Curved Surface Refraction

Question

A thin convex lens made from crown glass $(µ = \frac{3}{2})$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3} and \frac{5}{3}$ , it has the focal lengths f₁ and f₂ respectively. The correct relation between the focal lengths is :

f₁ = f₂ < f

f₁ and f₂ both become negative

f₁ > f and f₂ becomes negative

f₂ > f and f₁ becomes negative

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$\frac{1}{f} = (\frac{3}{2} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) = \frac{1}{2} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f_{1}} = (\frac{3 / 2}{4 / 3} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) = \frac{1}{8} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f_{2}} = (\frac{3 / 2}{5 / 3} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) = \frac{- 1}{10} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$