11. The wavelength of the light ray in air is 0.589 x 10⁻⁶ m.
12. Angle of incidence for the light ray at point P is 43.23°.
13. The absolute index of refraction for medium X is 1.46
What is Snell's law?
It states that the ratio of sine of angle of incidence and angle of refraction is equal to the refractive index of first medium to the second medium.
sini/sinr = n₁/n₂
11. The wavelength is related to the frequency as
λ = c/f
where c = 3 x 10⁸ m/s and frequency f = 5.09x 10¹⁴ Hz
Put the values, we get
λ = 3 x 10⁸/ 5.09x 10¹⁴
λ =0.589 x 10⁻⁶ m
Thus, the wavelength of the light ray in air is 0.589 x 10⁻⁶ m.
12. Given the angle of incidence is i, angle of refraction r =90° , n₂ = Refractive index of medium X = 1.46 and n₁ = Refractive index of air = 1
Substituting the values into Snell's law expression we get,
sin i= sin 90 x 1/1.46
i = 43.23 degrees
Thus, the angle of incidence is 43.23 degrees.
13. The refractive index is the ratio of speed of light in vacuum to the speed of light in the medium X.
n = c/v₂
If v₂ is the velocity of light in medium X, then
sin i / sin r = v₂/v₁
sin 43.23 / sin 90 = v₂/ 3 x 10⁸
v₂ = 2.055 x 10⁸ m/s
So, the refractive index be
n = 3 x 10⁸/2.055 x 10⁸
n = 1.46
Thus, absolute index of refraction for medium X is 1.46
Learn more about Snell's law.
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