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

To address the given question about the optical properties of a light pipe, we will evaluate each statement based on known principles of optics:

(A) Optical density of core should be greater than the optical density of cladding.
This statement is true. For a light pipe (optical fiber) to function correctly, total internal reflection must occur. This requires that light travel from a medium of higher optical density (the core) to one of lower optical density (the cladding).

(B) r and θ will always be equal.
This statement is false. In the context of refraction and total internal reflection, angles r (refraction angle) and θ (incidence or reflection angle) are not necessarily equal. They are determined by Snell's law which typically results in different values unless specified conditions are met.

(C) Optical density of cladding is \(\frac{\sinθ \sin i}{\sin r}\).
This statement is incorrect. The expression does not follow the general principles of optics for determining optical densities.

(D) Optical density of cladding is \(\frac{\sin r \sin i}{\sin θ}\).
This statement is also incorrect based on the same reasoning as in statement (C).

Given this analysis, the correct answer is (A) only, as it is the only true statement from the options provided.

Answer 2

• 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.