Question

The Brewster's angle \(\theta _{B}\) for air-glass interface should be such that
(refractive index of glass \(=\frac{3}{2}\))

• A. \(\theta _{B}=90^{\circ }\)
• B. \(45^{\circ }\lt \theta _{B}\lt 90^{\circ }\)
• C. \(30^{\circ }\lt \theta _{B}\lt 45^{\circ }\)
• D. \(0^{\circ }\lt \theta _{B}\lt 45^{\circ }\)

Hint:

Brewster's law gives the tangent of the angle equal to the refractive index, so compare the tangent value with those of known angles.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Brewster's law states that \(\tan\theta_{B} = \mu\), where \(\mu\) is the refractive index of the glass relative to air.

Step 2: Calculation
Here \(\tan\theta_{B} = \dfrac{3}{2} = 1.5\).
Since \(\tan 45^{\circ} = 1\) and \(\tan 90^{\circ}\) is infinite, a value of 1.5 lies between them.

Step 3: Result
So \(\theta_{B}\) is greater than \(45^{\circ}\) but less than \(90^{\circ}\) (about \(56.3^{\circ}\)).

Final Answer:
Brewster's angle lies between 45 degrees and 90 degrees. \[ \boxed{\text{(B) }45^{\circ}\lt\theta_{B}\lt 90^{\circ}} \]