The refractive index for glycerine is [tex]n_g=1.473[/tex], while for air it is [tex]n_a = 1.00[/tex].
When the light travels from a medium with greater refractive index to a medium with lower refractive index, there is a critical angle over which there is no refraction, but all the light is reflected. This critical angle is given by:
[tex]\theta_c = \arcsin ( \frac{n_2}{n_1} )[/tex]
where n1 and n2 are the refractive indices of the two mediums. If we susbtitute the refractive index of glycerine and air in the formula, we find the critical angle for this case:
[tex]\theta_c = \arcsin ( \frac{1.00}{1.473} )=42.8^{\circ}[/tex]
