Given Numerical Aperture (NA) = 0.30 and refractive index of core = 1.49,calculate the critical angle at the core–cladding interface

Given Numerical Aperture (NA) = 0.30 and refractive index of core = 1.49,
calculate the critical angle at the core–cladding interface.

Answer:-

Given:

• Numerical Aperture (NA) = 0.30
• Refractive Index of Core (n₁) = 1.49

Calculate the critical angle (θ_c) at the core–cladding interface.

Step 1: Find Refractive Index of Cladding (n₂)

We use the formula:
NA = √(n₁² - n₂²)

Rearranging:
n₂² = n₁² - NA² = (1.49)² - (0.30)² = 2.2201 - 0.09 = 2.1301
n₂ ≈ √2.1301 ≈ 1.459

Step 2: Calculate Critical Angle (θ_c)

Using Snell’s Law:
sin(θc) = n₂ / n₁ = 1.459 / 1.49 ≈ 0.9795
θc = sin⁻¹(0.9795) ≈ 78.56°

Final Answer:

θ_c ≈ 78.56°