If the focal lengths of red and violet light | vedclass

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Question

(A) According to the lens maker's formula,the focal length $f$ of a lens is given by $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \ri

Vedclass · Accepted Answer

$f_R > f_v$

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(A) According to the lens maker's formula,the focal length $f$ of a lens is given by $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.Since $\left( \frac{1}{R_1} - \frac{1}{R_2} \right)$ is constant for a given lens,we have $\frac{1}{f} \propto (\mu - 1)$,which implies $f \propto \frac{1}{\mu - 1}$.According to Cauchy's dispersion formula,the refractive index $\mu$ is higher for violet light than for red light,i.e.,$\mu_v > \mu_R$.Since $\mu_v > \mu_R$,it follows that $(\mu_v - 1) > (\mu_R - 1)$.Therefore,$\frac{1}{f_v} > \frac{1}{f_R}$,which implies $f_R > f_v$.

If the focal lengths of red and violet light rays for the same lens are $f_R$ and $f_v$ respectively,then which of the following is true?

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