Respuesta :
Answer:
Difference in the angle of refraction = 0.3°
41.04° is the minimum angle of incidence.
Explanation:
Angle of incidence = 38.0°
For yellow light :
Using Snell's law as:
[tex]\frac {sin\theta_2}{sin\theta_1}=\frac {n_1}{n_2}[/tex]
Where,
Θ₁ is the angle of incidence
Θ₂ is the angle of refraction
n₁ is the refractive index for yellow light which is 1.523
n₂ is the refractive index of air which is 1
So,
[tex]\frac {sin\theta_2}{sin{38.0}^0}=\frac {1.523}{1}[/tex]
[tex]{sin\theta_2}=0.9377[/tex]
Angle of refraction for yellow light = sin⁻¹ 0.9377 = 69.67°.
For green light :
Using Snell's law as:
[tex]\frac {sin\theta_2}{sin\theta_1}=\frac {n_1}{n_2}[/tex]
Where,
Θ₁ is the angle of incidence
Θ₂ is the angle of refraction
n₁ is the refractive index for green light which is 1.526
n₂ is the refractive index of air which is 1
So,
[tex]\frac {sin\theta_2}{sin{38.0}^0}=\frac {1.526}{1}[/tex]
[tex]{sin\theta_2}=0.9395[/tex]
Angle of refraction for green light = sin⁻¹ 0.9395 = 69.97°.
The difference in the angle of refraction = 69.97° - 69.67° = 0.3°
Calculation of the critical angle for the yellow light for the total internal reflection to occur :
The formula for the critical angle is:
[tex]{sin\theta_{critical}}=\frac {n_r}{n_i}[/tex]
Where,
[tex]{\theta_{critical}}[/tex] is the critical angle
[tex]n_r[/tex] is the refractive index of the refractive medium.
[tex]n_i[/tex] is the refractive index of the incident medium.
n₁ is the refractive index for yellow light which is 1.523 (incident medium)
n₂ is the refractive index of air which is 1 (refractive medium)
Applying in the formula as:
[tex]{sin\theta_{critical}}=\frac {1}{1.523}[/tex]
The critical angle is = sin⁻¹ 0.6566 = 41.04°
