Answer:
A) Material X is flint glass
B) Speed of light in the X material is 1.807 x [tex]10^{8}[/tex] m/s
C) Angle of refraction of light in medium X is [tex]29.57^{o}[/tex]
Explanation:
Given data:
frequency of the light f = 5.09 x [tex]10^{14}[/tex] Hz
angle of incidence Θ[tex]_{i}[/tex] = [tex]55^{o}[/tex]
index of refraction of material [tex]n_{2}[/tex] = 1.66
A) To find material X
Given the index of refraction is 1.66 and hence the material is the flint glass
B) To calculate the speed of light in the material.
We know that the relation between index of refraction (n), velocity of light (c = 3 x [tex]10^{8}[/tex] m/s) and velocity of light is given by the equation:
n = c/v
Hence,
Speed of light in the X material v = c/n
= [tex]\frac{3 x 10^{8} }{1.66}[/tex]
= 1.807 x [tex]10^{8}[/tex] m/s
C) To calculate angle of refraction of light in medium X
We know that the Snell's law states that
[tex]n_{1} sin[/tex] Θ[tex]_{i}[/tex] = [tex]n_{2} sin[/tex] Θ[tex]_{r}[/tex]
[tex]n_{1}[/tex] = incident index
[tex]n_{2}[/tex] = refracted index
Θ[tex]_{i}[/tex] = incident angle
Θ[tex]_{r}[/tex] = refracted angle
In given problem, [tex]n_{1}[/tex] = 1 since medium is air
Substituting the known values, we get
1 x [tex]sin[/tex] [tex]55^{o}[/tex] = 1.66 x [tex]sin[/tex] Θ[tex]_{r}[/tex]
[tex]sin[/tex] Θ[tex]_{r}[/tex] = [tex]sin[/tex] [tex]55^{o}[/tex] /1.66
= 0.4935
Hence, angle of refraction of light in medium X Θ[tex]_{r}[/tex] = [tex]sin^{-1}[/tex] (0.4935)
= [tex]29.57^{o}[/tex]
(A) The material is flint glass.
(B) The speed of light in the material is 1.8×10⁸ m/s.
(C) The angle of refraction is 33°.
It is given that the frequency of the light is, f = 5.09 × 10¹⁴ Hz
The angle of incidence is, i = 55°,
and the refractive index of the material X is, n = 1.66
(A) Since the refractive index of the unknown material is 1.66, if we compare it with the know data, we can conclude that the material is flint glass.
(B) The speed of light in air or vacuum is equal to c = 3×10⁸ m/s when it enters a medium of refractive index n, its speed becomes:
v = c/n
v = 3×10⁸/1.66
v = 1.8×10⁸ m/s
(C) According to Snell's law:
[tex]\frac{sin(i)}{sin(r)}=n[/tex]
where r is the angle of refraction, and
n is the refractive index of the material with respect to vacuum
[tex]\frac{sin(55)}{sin(r)}=1.66\\\\sin(r)=\frac{sin(55)}{1.66}\\\\ sin(r)=\frac{0.819}{1.66}=0.546[/tex]
r = 33°
Learn more about Snell's law:
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