(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:
The optical properties of a light pipe are assessed against established optical principles. Each statement is evaluated as follows:
(A) The optical density of the core must exceed that of the cladding. This assertion is correct. Effective light pipe (optical fiber) operation relies on total internal reflection, which necessitates light transitioning from a higher optical density medium (the core) to a lower optical density medium (the cladding).
(B) The angles r and θ will invariably be equal. This assertion is incorrect. In scenarios involving refraction and total internal reflection, angles r (angle of refraction) and θ (angle of incidence or reflection) do not inherently possess equal values. Their relationship is governed by Snell's Law, which generally yields differing results unless specific conditions are met.
(C) The optical density of the cladding is represented by \(\frac{\sinθ \sin i}{\sin r}\). This assertion is erroneous. The provided expression does not align with fundamental optical principles for determining optical densities.
(D) The optical density of the cladding is represented by \(\frac{\sin r \sin i}{\sin θ}\). This assertion is also erroneous, consistent with the reasoning applied to statement (C).
Based on this analysis, statement (A) alone is accurate, representing the sole correct proposition among the given options.
