Question

Una luz (con una longitud de onda de 600 nm y velocidad de la luz de c = 3 × 108 m⁄s), que proviene del aire incide en glicerina con un ángulo de 30°. Después de pasar por la glicerina, entra en diamante, después pasa por cuarzo y por último sale de nuevo al aire. Calcule el ángulo de refracción al pasar el rayo en cada medio, también calcule la velocidad de la luz en cada medio y la longitud de onda en cada medio

Answer 1

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

Step-by-step 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

`(c)/(\lambda_o) = (c)/(\lambda_n)`

λₙ =
`(v)/(c) \ \lambda_o`

λₙ = λ₀ / n

we used these expressions to our case

1) medium incident air n₁ = 1 medium transmitted n₂ = 1.473

sin θ₂=
`(n_1)/(n_2)` 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