Question

Which color of light has a higher critical angle? Red light or Green light.

Answer 1

Critical Angle $I_c$:

The angle of incidence (incident angle) in a denser medium (having greater refractive index) for which angle of refraction in the rarer medium is ${90}^o$ is called the critical angle.

${}_2{}^1\mu =\frac{1}{\sin I_c}=\cos ec{I}_c$

where ${}_2{}^1\mu$ is the refractive index of 2nd medium (denser medium) with respect to the 1st medium (rarer medium),

As we know red has a greater wavelength than green, thus, the refractive index of the medium of the green color is more than for the red color.

We also know the relation,

$\begin{array}{rcl}\mu & =& \frac{1}{\sin I_c}\\ {\mu }_{red}& <& {\mu }_{green}\\ {\left(\sin I_c\right)}_{red}& >& {\left(\sin I_c\right)}_{green}\\ {\left(I_c\right)}_{red}& >& {\left(I_c\right)}_{green}\end{array}$

Hence, red light has a higher critical angle.