Explanation:
It is given that,
The wavelength of red helium–neon laser light in air is, [tex]\lambda=632.8\ nm=632.8\times 10^{-9}\ m[/tex]
(a) Frequency, [tex]f=\dfrac{c}{\lambda}[/tex]
[tex]f=\dfrac{3\times 10^8\ m/s}{632.8\times 10^{-9}\ m}[/tex]
[tex]f=4.74\times 10^{14}\ Hz[/tex]
(b) Let [tex]\lambda_g[/tex] shows its wavelength in glass that has an index of refraction of 1.51,
[tex]\lambda_g=\dfrac{\lambda}{n}[/tex]
[tex]\lambda_g=\dfrac{632.8\times 10^{-9}\ m}{1.51}[/tex]
[tex]\lambda_g=4.19\times 10^{-7}\ m[/tex]
[tex]\lambda_g=419\ nm[/tex]
(c) Let [tex]v_g[/tex] is its speed in the glass.
[tex]v_g=\dfrac{c}{n}[/tex]
[tex]v_g=\dfrac{3\times 10^8\ m/s}{1.51}[/tex]
[tex]v_g=1.99\times 10^8\ m/s[/tex]
Hence, this is the required solution.