Answer:
Frequency of light = 5454.5 GHz
Refractive index = 1.46
speed of light in quartz = 2.05 x 10^8 m/s
Step-by-step 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