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A glass plate 2.50 mm thick, with an index of refraction of 1.40, is placed between a source of light with wavelength 540 nm (in vacuum) and a screen. The source is 1.80 cm from the screen.

How many wavelengths are there between the source and the screen?

(HINT: the wavelength of light inside the glass is different!)

Respuesta :

Answer:

[tex]N=0.194[/tex]

Explanation:

Given:

  • refractive index of the glass plate, [tex]n=1.4[/tex]
  • thickness of the glass plate, [tex]x=2.5\ mm[/tex]
  • wavelength of the source light, [tex]\lambda=18\ mm[/tex]

We know that the refractive index of a medium is given as:

[tex]\rm n=\frac{wavelength\ of\ light\ in\ the\ air\ or\ vacuum}{wavelength\ of\ light\ in\ the\ medium}[/tex]

[tex]n=\frac{\lambda}{\lambda'}[/tex]

[tex]1.4=\frac{18}{\lambda'}[/tex]

[tex]\lambda'\approx12.857\ mm[/tex]

Hence the no. of wavelengths in the glass:

[tex]N=\frac{x}{\lambda'}[/tex]

[tex]N=\frac{2.5}{12.857}[/tex]

[tex]N=0.194[/tex]