A light wave has a frequency of \( 4\times10^{14}\,\mathrm{Hz} \). Find the difference in its wavelengths in alcohol of refractive index 1.35 and glass of refractive index 1.5:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 556 Å
The frequency of light does not change when it enters a medium, but its speed does, so its wavelength in a medium of refractive index n is \( \lambda = \frac{v}{f} = \frac{c}{nf} \).
Wavelength in alcohol
\( \displaystyle \lambda_a = \frac{3\times10^{8}}{1.35\times4\times10^{14}} = 5.556\times10^{-7}\,\mathrm{m} \)
Wavelength in glass
\( \displaystyle \lambda_g = \frac{3\times10^{8}}{1.5\times4\times10^{14}} = 5.000\times10^{-7}\,\mathrm{m} \)
Difference
\( \Delta\lambda = (5.556-5.000)\times10^{-7}\,\mathrm{m} = 5.56\times10^{-8}\,\mathrm{m} \)
\( \displaystyle \Delta\lambda = \frac{5.56\times10^{-8}}{10^{-10}}\,\mathrm{\mathring{A}} = 556\,\mathrm{\mathring{A}} \)