Respuesta :
ANSWER
[tex]\begin{gathered} (a)\text{ }38.8\degree \\ (b)\text{ }38\degree \end{gathered}[/tex]EXPLANATION
Parameters given:
Incident angle of white light, θ1 = 71.2 degrees
Speed of red light in the prism, vr = 1.984 * 10^8 m/s
Speed of violet light in the prism, vv = 1.951 * 10^8 m/s
Speed of light in air, v = 3 * 10^8 m/s
(a) To find the angle at which the red light enters the prism, apply the relationship given by Snell's law:
[tex]{\frac{v}{v_r}}=\frac{\sin\theta_1}{\sin\theta_r}[/tex]where v = speed of light in air
vr = speed of red light in the prism
θr = angle of refraction (angle that the light enters the prism)
Hence, solving for θr, we have that the angle at which the red light enters the prism is:
[tex]\begin{gathered} \frac{3*10^8}{1.984*10^8}=\frac{\sin71.2}{\sin\theta_r} \\ \\ \sin\theta_r=\frac{1.984*\sin71.2}{3}=0.6261 \\ \\ \theta_r=\sin^{-1}(0.6261) \\ \theta_r=38.8\degree \end{gathered}[/tex]That is the answer.
(b)To find the angle at which the violet light enters the prism, apply the same formula above for violet light:
[tex]\frac{v}{v_v}=\frac{\sin\theta_1}{\sin\theta_v}[/tex]Hence, solving for θv, we have that the angle at which the violet light enters the prism is:
[tex]\begin{gathered} \frac{3*10^8}{1.951*10^8}=\frac{\sin71.2}{\sin\theta_v} \\ \\ \sin\theta_v=\frac{1.951*\sin71.2}{3}=0.6156 \\ \\ \theta_v=\sin^{-1}(0.6156) \\ \theta_v=38\degree \end{gathered}[/tex]That is the answer.
