Answer:
The angle of refraction is closest to [tex]45^{o}[/tex]
Explanation:
Snell's law compares the ratios of the angles of incident and refraction, and it would be applied in solving this problem.
Given the
Refractive index η= 1.42
angle of incident = i
angle of refraction = r = 1/2 x i = i/2
applying Snell's law;
η = [tex]\frac{sini}{sin\frac{i}{2} }[/tex]
applying trigonometric identity (sin 2x=2sinxcosx )
sin 2i = 2sinicosi
1.42 = [tex]\frac{2 sin(i/2)cos(i/2)}{sin (i/2) }[/tex]
cos i/2 = 1.42/2
cos i/2 = 0.71
i/2 = [tex]cos^{-1}[/tex] 0.71 = [tex]44.765^{o}[/tex]
i/2 ≈ [tex]45^{o}[/tex]
Therefore the angle of refraction is closest to [tex]45^{o}[/tex]
