Answer:
A) Material X is flint glass
B) Speed of light in the X material is 1.807 x
m/s
C) Angle of refraction of light in medium X is 
Explanation:
Given data:
frequency of the light f = 5.09 x
Hz
angle of incidence Θ
= 
index of refraction of material
= 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
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
= 
= 1.807 x
m/s
C) To calculate angle of refraction of light in medium X
We know that the Snell's law states that
Θ
=
Θ
= incident index
= refracted index
Θ
= incident angle
Θ
= refracted angle
In given problem,
= 1 since medium is air
Substituting the known values, we get
1 x
= 1.66 x
Θ
Θ
=
/1.66
= 0.4935
Hence, angle of refraction of light in medium X Θ
=
(0.4935)
= 