The statement that light travels in straight lines (rectilinear propagation of light) holds true only when the medium through which light travels has what nature?

Introduction / Context:
One of the basic laws taught in geometrical optics is the rectilinear propagation of light, which states that light travels in straight lines. This principle is used in explaining the formation of shadows, pinhole images and the apparent straight line paths of light rays in simple media. However, this statement is an approximation that holds only under certain conditions. When the optical properties of the medium vary in space, light rays can bend gradually rather than travel in straight lines. This question asks you to identify the conditions on the medium for which the statement that light travels in straight lines remains valid.

Given Data / Assumptions:
• The medium refers to the material through which light propagates. • The options describe mediums with constant (homogeneous) or varying (inhomogeneous) refractive indices. • Transparency is required for light to propagate without strong scattering or absorption. • We focus on macroscopic ray paths rather than microscopic scattering events.

Concept / Approach:
Rectilinear propagation of light is strictly valid in a homogeneous and isotropic medium that is transparent, meaning its refractive index is the same everywhere and in all directions, and it does not scatter light significantly. In such a medium, Snell law applied locally tells us that light rays go straight until they encounter a boundary with a different refractive index. In inhomogeneous media where the refractive index changes with position, such as in the atmosphere with temperature gradients, rays can bend continuously, producing mirages and other effects. In layered media made of slabs, rays change direction at each interface. Thus, the simple statement that light travels in straight lines holds only for homogeneous, transparent media.

Step-by-Step Solution:
Step 1: Recall that a homogeneous medium has the same refractive index at every point. Step 2: Understand that in such a medium, there are no internal boundaries or gradients to bend light rays. Step 3: Recognise that transparency means light can travel through without severe scattering or absorption, preserving well defined ray paths. Step 4: Note that in inhomogeneous media where refractive index varies, such as hot air near a road, light rays refract gradually and curve rather than remaining straight. Step 5: Note that in layered slabs of different refractive indices, rays travel straight within each layer but bend at interfaces, so overall paths are kinked, not strictly straight. Step 6: Conclude that the rectilinear propagation law strictly holds only in a homogeneous and transparent medium.

Verification / Alternative check:
Everyday examples support this interpretation. In calm, clear air, shadows of objects have sharp edges, consistent with straight line travel of light. In contrast, near hot surfaces such as asphalt roads on sunny days, shimmering and distorted images arise because temperature gradients cause gradual refractive index changes that bend light rays, violating simple straight line propagation. Optical fibres deliberately use refractive index gradients or core claddings to bend light paths. These phenomena show that when the medium is not homogeneous, light does not follow straight lines in the simple sense assumed in geometrical optics. Therefore, the requirement for homogeneity and transparency is essential for rectilinear propagation to hold as an approximation.

Why Other Options Are Wrong:
Option A, a medium of variable refractive index, explicitly contradicts the condition needed for straight line travel; such variation causes rays to curve. Option B, slabs of different refractive indices, leads to multiple refractions at interfaces, producing broken or zigzag paths rather than a single straight path. Option D, an inhomogeneous but transparent medium, again allows light to propagate but with curved or distorted rays due to spatial changes in index. These media do not satisfy the strict condition that light travels in straight lines throughout the region, so they are not consistent with the simple rectilinear propagation statement.

Common Pitfalls:
Students sometimes overgeneralise the idea of rectilinear propagation and assume that light always travels in straight lines no matter what the medium is like. This can lead to confusion when learning about atmospheric refraction, mirages and graded index fibres. Another pitfall is to ignore the role of transparency and think that any homogeneous medium, even a strongly scattering one, would preserve straight rays, when in practice scattering destroys the simple ray model. Remember that rectilinear propagation is a useful approximation that applies to clear, homogeneous media, and that deviations from these conditions naturally lead to bending or diffusion of light rays.

Final Answer:
The correct choice is A homogeneous and transparent composition, because light travels in straight lines only in media with uniform refractive index and sufficient transparency, whereas variations in refractive index or layered structures cause rays to bend or change direction.