Answer:
(a) 42.28°
(b) 37.08°
Explanation:
From the principle of refraction of light, when light wave travels from one medium to another medium, we have:
[tex]\frac{n_{b} }{n_{a} }[/tex] = sinθ[tex]_{a}[/tex]/sinθ[tex]_{b}[/tex]
In the given problem, we are given the refractive indices of light which are parallel and perpendicular to the axis of the optical lens as 1.4864 and 1.6584 respectively.
For critical angle θ[tex]_{a}[/tex] = θ[tex]_{c}[/tex], θ[tex]_{b}[/tex] = 90°; [tex]n_{b} = 1[/tex]
(a) [tex]n_{a} = 1.4864[/tex]
[tex]\frac{1 }{1.4864 }[/tex] = sinθ[tex]_{c}[/tex]/sin90°
0.6728 = sinθ[tex]_{c}
θ[tex]_{c} = sin^(-1) 0.6728 = 42.28°
(b) [tex]n_{a} = 1.6584[/tex]
[tex]\frac{1 }{1.6584}[/tex] = sinθ[tex]_{c}[/tex]/sin90°
0.60299 = sinθ[tex]_{c}
θ[tex]_{c} = sin^(-1) 0.60299 = 37.08°
