Question
Download Solution PDFA light ray enters through a right angled prism at point P with the angle of incidence 30° as shown in figure. It travels through the prism parallel to its base BC and emerges along the face AC. The refractive index of the prism is:
Answer (Detailed Solution Below)
Option 2 : \(\frac{\sqrt5}{2}\)
Detailed Solution
Download Solution PDFCalculation:
The formula for the refractive index is given as:
r1 + c = A
⇒ r1 = 90 - c
Snell's law at the emergent boundary
Sin(c) = 1 / μ
⇒ Cos(c) = (μ2 - 1)1/2 / μ
According to Snell's law at incident boundary
Sin(30) = μ × Sin(r1)
1/2 = μ × Sin(90 - c) =μ Cos(c)
⇒ 1/2 = μ × (μ2 - 1)1/2 / μ
Squaring both sides:
1/4 = μ2 - 1
μ2 = 5 / 4
μ = √(5 / 4) = √5 / 2
Thus, the correct option is option 2: μ = √5 / 2