1. What is the frequency of blue light that has a wavelength of 450 nm?
2. What is the frequency of red light that has a wavelength of 650 nm?
3. What is the index of refraction of a material in which the red-light wavelength is 450 nm?

• Wavelength of blue light is ${\lambda }_{blue}=450nm$
• Wavelength of the red light is ${\lambda }_{red}=650nm=6.5\times {10}^{-7}m$
• Speed of light in vacuum is $c=3\times {10}^{8}m/s$

Frequency is defined as the complete waves travelling per unit second.

The formula to calculate the frequency is given by

$f_{blue}=\frac{c}{{\lambda }_{blue}}$

Substitute $3\times {10}^{8}m/s$for c and $4.5\times {10}^{-7}m$for ${\lambda }_{blue}$to calculate the frequency of blue light.

$$\begin{gathered} f_{blue}=\frac{3\times {10}^{8}m/s}{4.5\times {10}^{-7}m} \\ =6.67\times {10}^{14}Hz \end{gathered}$$

The formula to calculate the frequency of red light is given by

$f_{red}=\frac{c}{{\lambda }_{red}}$

Substitute $3\times {10}^{8}m/s$for c and $6.5\times {10}^{-7}m$for ${\lambda }_{red}$to calculate the frequency of red light.

$$\begin{gathered} f_{red}=\frac{3\times {10}^{8}m/s}{6.5\times {10}^{-7}m} \\ =4.62\times {10}^{14}Hz \end{gathered}$$

The formula to calculate the refractive index of a material is given by

$n=\frac{c}{v}$

Since$v=f\lambda$,$n=\frac{c}{\lambda f}$.

Substitute $3\times {10}^{8}m/s$for c, $4.5\times {10}^{-7}mfor\lambda$and $4.62\times {10}^{14}Hz$for f to calculate the refractive index of the material.

$$\begin{gathered} n=\frac{3\times {10}^{8}m/s}{4.5\times {10}^{-7}m\times 4.62\times {10}^{14}Hz} \\ =1.443 \end{gathered}$$