Using, $c=\nu\lambda$

Let, $\nu _1$ be the frequency of the Red light.

$\lambda _1$ be the wavelength of the Red light.

$\nu _2$ be the frequency of the Violet light.

$\lambda _2$ be the wavelength of the Violet light.

Since, $\large\nu \propto \frac{1}{\lambda};\;\;\;\;\large\frac{\nu _1}{\nu _2}=\frac{\lambda_2}{\lambda_1}$

$\large\frac{\nu _1}{\nu _2}=\frac{4.10\times 10^{-5}}{6.56\times 10^{-5}}$$ = 0.625$

Now the energy associated with electromagnetic radiation is given by $E=h\nu$

$=\large\frac{E_1}{E_2}=\large\frac{\nu_1}{\nu_2}=\frac{\lambda_1}{\lambda_2}$$=0.625$

$\therefore$ Hence the ratio of energies is same as that of the frequencies

Hence (c) is the correct answer.