Answer:
Explanation:
Refractive index f the medium, n = t
Let the angle of incidence is i
(a) As given in the question, the angle of refraction is half of angle of incidence.
Let the angle of refraction is r
r = i / 2
By use of Snell's law
[tex]n = \frac{Sin i}{Sin r}[/tex]
By substituting the values, we get
[tex]t = \frac{Sin i}{Sin \frac{i}{2}}[/tex]
By using the formula of trigonometry
Sin2Ф = 2 SinФ CosФ
So, [tex]t = \frac{2Sin \frac{i}{2}\times Cos\frac{i}{2}}{Sin \frac{i}{2}}[/tex]
[tex]t = 2Cos\frac{i}{2}[/tex]
(b) For glass, the value of refractive index is 1.5, so the above expression becomes
[tex]1.5 = 2Cos\frac{i}{2}[/tex]
[tex]Cos\frac{i}{2}=0.75[/tex]
[tex]\frac{i}{2}=41.4[/tex]
i = 82.8°
