Answer: 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.
[tex]2nt = m \lambda[/tex]
For crystalline quartz: [tex]2n_{q}t_{q} = m \lambda_{q}[/tex]
For glycerine: [tex]2n_{g}t_{g} = n \lambda_{g}[/tex]
Here, m = n and [tex]\lambda_{q} = \lambda_{g}[/tex]
So, the ratio of both these values can be written as follows.
[tex]\frac{2n_{q}t_{q}}{2n_{g}t_{g}} = \frac{m \lambda_{q}}{n \lambda_{g}} = 1[/tex]
So, [tex]n_{q}t_{q} = n_{g}t_{g}[/tex]
[tex]\frac{t_{q}}{t_{g}} = \frac{n_{g}}{n_{q}} = \frac{1.473}{1.544}[/tex]
[tex]\frac{t_{q}}{t_{g}} = 0.954[/tex]
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.
