Respuesta :
Answer:
θ₁ = 35.32°
Explanation:
given,
refractive index of medium 1 = n₁ = 1.75
refractive index of medium 2 = n₂ = 1.24
condition to describe the refracted angle
[tex]\theta_{refracted} + \theta_{reflected}=90^0[/tex]
[tex]\theta_2 = 90^0-\theta_1[/tex]...(1)
Using Snell's Law
n₁ sin θ₁ = n₂ sin θ₂
θ₁ , θ₂ is the angle of incidence and refractive index
n₁. n₂ is the refractive index medium 1 and medium 2
1.75 x sin θ₁ = 1.24 x sin θ₂
From equation (1)
1.75 x sin θ₁ = 1.24 x sin (90-θ₁)
1.75 sin θ₁ = 1.24 cos θ₁
tan θ₁ = 0.708
θ₁ = 35.32°
Hence, angle of incidence is equal to θ₁ = 35.32°
The minimum angle with respect to the normal must the ray be incident on the interface in order to be totally internally reflected is;
i = 35.32°
We are given;
Index of refraction of medium 1; n₁ = 1.75
Index of refraction of medium 2; n₂ = 1.24
Now, since we want to find out the minimum angle for the ray on the interface to be internal reflected, it means that;
r + i = 90°
Where;
r is angle of refraction
i is angle of incidence
Now, the equation to find i will be from the formula for total internal reflection from snell's law which is;
n₁/n₂ = sin r/sin i
Where;
r is angle of refraction
i is angle of incidence
We are given;
n₁ = 1.75
n₂ = 1.24
Thus;
1.75/1.24 = (sin r)/(sin i)
Earlier, we saw that;
i + r = 90°
Thus;
r = 90 - i
Thus;
1.75/1.24 = (sin (90 - i))/(sin i)
In trigonometry, sin (90 - θ) = cos θ
Thus;
1.75/1.24 = (cos i))/(sin i)
1.75/1.24 = 1/(tan i)
i = tan^(-1) (1.24/1.75)
i = 35.32°
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