Answer :
Answer:
Difference in the angle of refraction = 0.5163°
41.1399 is the minimum angle of incidence.
Explanation:
Angle of incidence = 30.9°
For blue 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 blue light which is 1.531
n₂ is the refractive index of air which is 1
So,
[tex]\frac {sin\theta_2}{sin{30.9}^0}=\frac {1.531}{1}[/tex]
[tex]{sin\theta_2}=0.7862[/tex]
Angle of refraction for blue light = sin⁻¹ 0.7862 = 51.8318°.
For red 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 red light which is 1.520
n₂ is the refractive index of air which is 1
So,
[tex]\frac {sin\theta_2}{sin{30.9}^0}=\frac {1.520}{1}[/tex]
[tex]{sin\theta_2}=0.7806[/tex]
Angle of refraction for red light = sin⁻¹ 0.7806 = 51.3155°.
The difference in the angle of refraction = 51.8318° - 51.3155° = 0.5163°
Calculation of the critical angle for the red 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 red light which is 1.520 (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}{1.520}[/tex]
The critical angle is = sin⁻¹ 0.6579 = 41.1399°