Respuesta :
Answer:
a) angles 19.8º, 11.9º, 13.8, 20.4
b) speed 3 10⁸ m/s, 2,037 10⁸ m/s, v = 1.24 10⁸ m/s, v = 2.06 10⁸ m/s
c) wavelength 600 nm, 407.3 nm, 248.0 nm, 411.5 nm
Explanation:
For this exercise let's use the law of refraction
n₁ sin θ₁ = n₂ sin θ₂
where subscript 1 is for the middle of the incident ray and subscript 2 for the middle of the refracted ray
the refractive index is related to the speed of the lightning in the middle
n = c / v
When the ray enters a material medium, it is absorbed and re-emitted by the atoms in the medium, the frequency remains constant, it is a resonant system, but as the speed of light changes in the medium, the wavelength must change to keep the equation
in the void
c = λ f
in the material medium
v = λ f
[tex]\frac{c}{\lambda_o} = \frac{c}{\lambda_n}[/tex]
λₙ = [tex]\frac{v}{c} \ \lambda_o[/tex]
λₙ = λ₀ / n
we used these expressions to our case
1) medium incident air n₁ = 1 medium transmitted n₂ = 1.473
sin θ₂= [tex]\frac{n_1}{n_2}[/tex] sin θ₁
sin θ₂ = 1/1,473 sin 30
θ₂ = sin⁻¹ 0.3394
θ₂ = 19.8º
2) medium incident glycerin θ₁ = 19.8, medium transmitted diamond θ₂=2.419
sin θ₂ = 1.473/2.419 sin 19.8
θ₂ = sin⁻¹ 0.2067
θ₂ = 11.9º
3) half incident diamond θ₁ = 11.9º, half transmitted quartz n₂ = 1.458
sin θ₂= 2.419/1.458 sin 11.9
θ₂ = sin⁻¹ 0.3429
θ₂ = 13.8º
4) half incident quartz θ₁ = 13.8, medium transmitted air n₂ = 1
sin θ₂ = 1.458/1 sin 13.8
θ₂ = sin⁻¹ 0.3467
θ₂ = 20,4º
b) we look for the speed of lightning in each medium
air v = c = 3 10⁸ m / s
glycerin v = c / n
v = 3 108 / 1,473
v = 2,037 10⁸ m / s
diamond v = 3 108 / 2.419
v = 1.24 10⁸ m / s
quartz v = 3 108 / 1.458
v = 2.06 10⁸ m / s
c) the wavelength in each medium
air λₙ = λ₀/ n
λₙ = 600/1
λₙ 600 nm
glycerin
λₙ = 600 / 1,473
λₙ = 407.3 nm
Diamond
λₙ = 600 / 2.419
λₙ = 248.0 nm
quartz
λₙ = 600 / 1.458
λₙ = 411.5 nm
