106,185 views
42 votes
42 votes
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 =

User Edlin
by
3.2k points

1 Answer

14 votes
14 votes

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=(\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:


{(d_p)/(\lambda_p)}=(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} (d_p)/((\lambda)/(n_p))=(d_f)/((\lambda)/(n_f)) \\ \\ (d_p)/(d_f)=((\lambda)/(n_p))/((\lambda)/(n_f)) \\ \\ (d_p)/(d_f)=(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} (d_p)/(d_f)=(1.66)/(1.49) \\ \\ (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

User Gylaz
by
2.9k points