Question

For a light pipe as shown in the figure:

(A) Optical density of core should be greater than the optical density of cladding.
(B) r and θ will always be equal.
(C) Optical density of cladding is \(\frac{sinθ sin i}{sin r}\).
(D) Optical density of cladding is \(\frac{sin r sin i }{sin θ}.\)
Choose the correct answer from the options given below:

• A. (A), (B), and (D) only
• B. (A), (B), and (C) only
• C. (A) only
• D. (B), (C), and (D) only

Answer 1

The Correct Option is C

• Total internal reflection requires: n_core > n_cladding
• Critical angle θ_c = sin^-1(n_cladding/n_core)
• Snell's law governs refraction at boundaries: n₁sinθ₁ = n₂sinθ₂

Analysis of Each Statement:

(A) Optical density of core > cladding:

• Essential for total internal reflection
• Core must have higher refractive index than cladding
• Correct

(B) Angles r and θ always equal:

• Only true for normal incidence (special case)
• Generally not equal for oblique incidence
• Incorrect

(C) Optical density of cladding = sinθ·sin i / sin r:

• From Snell's law: n_cladding = n_coresinθ/sin r
• Missing n_core term in given expression
• Incorrect

(D) Optical density of cladding = sin r·sin i / sinθ:

• Doesn't match any valid optical relationship
• Incorrect dimensional analysis (units don't match refractive index)
• Incorrect

Correct Statements:

Only (A) is correct.

Answer 2

In a light pipe, total internal reflection occurs when the refractive index (or optical density) of the core is greater than that of the cladding. This allows the light to be confined within the core. The angles r and θ depend on Snell’s law, and they are not always equal. Therefore, only statement (A) is correct.