The Sun emits a ray of light with a wavelength of 550 nm. a. What is its frequency?b. The ray falls on a flat piece of quartz at an angle of 70º relative to the surface. The ray refracts to an angle of 76.46º relative to the surface. What is the index of refraction for quartz?c. What is the speed of light in quartz?

Frequency of light = 5454.5 GHz

Refractive index = 1.46

speed of light in quartz = 2.05 x 10^8 m/s

Explanation:

The wavelength of the light λ = 550 nm = 550 x 10^-9 m

frequency = ?

Frequency of light f = c/λ

where

c is the speed of light = 3 x 10^8 m/s

substituting, we have

f = (3 x 10^8)/(550 x 10^-9)

frequency f = 5.4545 x 10^14 Hz

==> 5454.5 GHz

The relationship between refractive index is given as

n1 sinθ1 = n2 sinθ2

where

n1 is the refractive index of air = 1

θ1 is the angle of incidence = (90 -70) = 20°

θ2 is the angle of refraction = (90 - 76.46) = 13.54°

n2 is the refractive index of quartz

substituting values, we have

1 x sin 20 = n2 x sin 13.54

0.3420 = n2 x 0.2341

refractive index of quartz n2 = 0.3420/0.2341 = 1.46

From n = c/v

where

n is the refractive index of quartz

c is the speed of light in air = 3 x 10^8 m/s

v is the speed of light in quartz = ?

substituting values, we have

1.46 = (3 x 10^8)/v

v = (3 x 10^8)/1.46 = 2.05 x 10^8 m/s

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