If the focal length of a double convex lens f | vedclass

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(C) According to the Lens Maker's Formula,the focal length $f$ is given by $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.This

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Less than $f_R$

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(C) According to the Lens Maker's Formula,the focal length $f$ is given by $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.This implies $f \propto \frac{1}{\mu - 1}$.According to Cauchy's dispersion formula,the refractive index $\mu$ is inversely proportional to the wavelength $\lambda$ $(\mu \propto \frac{1}{\lambda})$.Since the wavelength of violet light $(\lambda_V)$ is less than the wavelength of red light $(\lambda_R)$,the refractive index for violet light $(\mu_V)$ is greater than the refractive index for red light $(\mu_R)$.As $\mu_V > \mu_R$,it follows that $(\mu_V - 1) > (\mu_R - 1)$.Since $f$ is inversely proportional to $(\mu - 1)$,a larger refractive index results in a smaller focal length.Therefore,the focal length for violet light $(f_V)$ is less than the focal length for red light $(f_R)$.

If the focal length of a double convex lens for red light is $f_R$,what is its focal length for violet light?

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