If light from a 560-nm monochromatic source in air is incident upon the surface of fused quartz (n = 1.56)at an angle of 60 $\degree$,what is the wavelength of the ray refracted within the quartz?
A)192 nm
B)359 nm
C)560 nm
D)874 nm

Question

Quizplus · Accepted Answer

Using Snell's law, we can find the angle of refraction:

n_air sin(theta_i) = n_quartz sin(theta_r)

where n_air is the refractive index of air (approx. 1), n_quartz is the refractive index of fused quartz (1.56), theta_i is the angle of incidence (60 degrees), and theta_r is the angle of refraction.

Plugging in the values, we get:

1 x sin(60) = 1.56 x sin(theta_r)

theta_r ≈ 38.6 degrees

Next, we can use the formula for the wavelength of light in a material:

lambda_quartz = lambda_air/n_quartz

where lambda_air is the wavelength in air and lambda_quartz is the wavelength in fused quartz.

Plugging in the values, we get:

lambda_quartz = 560 nm/1.56 ≈ 359 nm

So the ray refracted within the quartz has a wavelength of 359 nm, which is closest to choice B.

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