Light of unknown wavelength in vacuum enters a transparent liquid from air. Let n be the refractive index of the liquid with respect to air.
(i) Derive, in symbolic form, an expression for the ratio of the wavelengths of the light in air and in the liquid in terms of n.
(ii) If the measured wavelength inside the liquid is 440nm and n=1.33, calculate its wavelength in air as well as its frequency.
(iii) The light now passes from the first liquid into a second liquid of refractive index 1.20 (with respect to air). Without finding the wavelength in air again, determine directly the wavelength in the second liquid.
(iv) Comment on how your derivation in part (i) simplifies multi-step wavelength calculations during successive transitions between media.