Question

What is the ratio of thicknesses of polystyrene and flint glass that would contain the same number of wavelengths of light? (Use any necessary data found in this table.)tpolystyrene/flint glass =

Answer 1

Let's find the ratio of thickness of polystyrene and flint glass that would contain the same number of wavelengths of light.

The relation of wavelength for any given medium is:

$\lambda_n=\frac{\lambda}{n}$

Where:

λn is the wavelength of the wave medium.

λ is the wavelength in vacuum.

n is the refractive index of the medium.

Now, for the thickness, we have:

${\frac{d_p}{\lambda_p}}=\frac{d_f}{\lambda_f}$

dp is the thickness of of polystyrene

df is the thickness of flint glass.

λp is the wavelength of light in polystyrene.

λf is the wavelength of light in flint glass.

Substitute λ/np for λp and λ/nf for λf:

$\begin{gathered} \frac{d_p}{\frac{\lambda}{n_p}}=\frac{d_f}{\frac{\lambda}{n_f}} \\ \\ \frac{d_p}{d_f}=\frac{\frac{\lambda}{n_p}}{\frac{\lambda}{n_f}} \\ \\ \frac{d_p}{d_f}=\frac{n_f}{n_p} \end{gathered}$

Where:

nf is the refractive index of flint glass = 1.66

n is the refractive index of polystyrene = 1.49

Thus, we have:

$\begin{gathered} \frac{d_p}{d_f}=\frac{1.66}{1.49} \\ \\ \frac{d_p}{d_f}=1.114 \end{gathered}$

Therefore the ratio of thicknesses of polystyrene and flint glass that would contain the same number of wavelengths of light is 1.114

ANSWER:

1.114