What is the ratio of thicknesses of glycerine (refractive index 1.473) to crystalline quartz (refractive index 1.544) such that they would contain the same number of wavelengths of 646nm light

The ratio of thicknesses of glycerine (refractive index 1.473) to crystalline quartz (refractive index 1.544) is 0.954.

Explanation:

Given: Refractive index of glycerine = 1.473

Refractive index of crystalline quartz = 1.544

Formula used is as follows.

For crystalline quartz:

For glycerine:

Here, m = n and

So, the ratio of both these values can be written as follows.

So,

Thus, we can conclude that the ratio of thicknesses of glycerine (refractive index 1.473) to crystalline quartz (refractive index 1.544) is 0.954.