Answer:
34.74
Explanation:
Critical angle is represented by the formula
θ(c) = sin^-1 (n2/n1)
And we have been given that the critical angle is 53.7, so we substitute
53.7 = sin^-1 (n2/n1), rearranging, we have
Sin 53.7 = n2/n1
0.8059 = n2/n1
Again, we know that the second medium is air, and the refractive index of air is 1, so
0.8059 = 1/n1, making n1 subject of formula
n1 = 1/0.8059
n1 = 1.24
Now, we have gotten both indices, using Snell's law of refraction, we then find the needed refraction
Sin θ(r) = n(i)/n(r) Sin θ(i)
Now, solving, we have
Sin θ(r) = 1/1.24 * sin 45
Sin θ(r) = 0.8059 * 0.7071
Sin θ(r) = 0.5699
θ(r) = Sin^-1 0.5699
θ(r) = 34.74
