Red light of wavelength 750 nm enters a glass plate of refractive index 1.5. If the velocity of light in vacuum is 3 × 10⁸ m/s, calculate in the glass (i) frequency (ii) velocity and (iii) wavelength of light.

Given,
Refractive index of glass plate, n_g = 1.5
Wavelength of light in vacuum, λ_v = 750 nm = 750 × 10^-9 m 
Velocity of light in vacuum, c = 3 × 10⁸ ms^-1 

Frequency of light in vacuum, 

                      $$\begin{gathered} \mathrm{\nu } = \frac{\mathrm{c}}{{\mathrm{\lambda }}_{\mathrm{v}}} \\ = \frac{3\times {10}^8 {\mathrm{ms}}^{-1}}{750 \times {10}^{-9}\mathrm{m}} \\ = 4\times {10}^{14} \mathrm{Hz} \end{gathered}$$  

For the light refracted in glass, frequency v remains unchanged but, wavelength and speed changes.

(i) Frequency of light in glass = Frequency of light in vacuum $= 4 \times {10}^{14} \mathrm{Hz}$ 

(ii) Velocity of light in glass, ${\mathrm{v}}_{\mathrm{g}} = \frac{\mathrm{c}}{{\mathrm{n}}_{\mathrm{g}}} = \frac{3 \times {10}^8 {\mathrm{ms}}^{-1}}{1.5} = 2 \times {10}^8 {\mathrm{ms}}^{-1}$ 

(iii) Wavelength of light in glass, ${\mathrm{\lambda }}_{\mathrm{g}} = \frac{{\mathrm{\lambda }}_{\mathrm{v}}}{{\mathrm{n}}_{\mathrm{g}}} = \frac{750 \mathrm{nm}}{1.5} = 500 \mathrm{nm}.$