A light beam travels at 1.94×108 in quartz. The wavelength of the light in quartz is 355 .Part AWhat is the index of refraction of quartz at this wavelength?Part BIf this same l…

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asked Sep 22, 2020 3.8k views

1 Answer

Jimwan · Answer 1 · 2020-09-27T08:24:51+0000

A) 1.55

The speed of light in a medium is given by:

v=(c)/(n)

where

$c=3\cdot 10^8 m/s$ is the speed of light in a vacuum

n is the refractive index of the material

In this problem, the speed of light in quartz is

$v=1.94\cdot 10^8 m/s$

So we can re-arrange the previous formula to find n, the index of refraction of quartz:

$n=(c)/(v)=(3\cdot 10^8 m/s)/(1.94\cdot 10^8 m/s)=1.55$

B) 550.3 nm

The relationship between the wavelength of the light in air and in quartz is

$\lambda=(\lambda_0)/(n)$

where

$\lambda$ is the wavelenght in quartz

$\lambda_0$ is the wavelength in air

n is the refractive index

For the light in this problem, we have

$\lambda=355 nm\\n=1.55$

Therefore, we can re-arrange the equation to find
$\lambda_0$ , the wavelength in air:

$\lambda_0 = n\lambda=(1.55)(355 nm)=550.3 nm$