==== Rectilinear propagation of light ====

The law of rectilinear propagation of light states that light travels in straight lines in an isotropic, homogeneous medium. It is a fundamental principle of geometric optics and accounts for common optical phenomena such as shadows, solar eclipses, and pinhole imaging..\\
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^  Shadow  ^  Solar Eclipse  ^  Pinhole Imaging  ^

The law of rectilinear propagation of light can be derived from Fermat's principle, which states that light follows a path for which the optical path length is stationary.
The optical path length is defined as the integral of the refractive index along the geometrical path. In a homogeneous medium, where the refractive index is constant, the optical path length is proportional to the geometrical length of the path.

For two fixed points, the straight‑line path has the shortest geometrical length and therefore the shortest optical path length. Thus, light travels in a straight line.

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The properties of the medium can modify the trajectories of light rays:
  *  **Homogeneous medium:** The refractive index is spatially uniform, and light rays do not bend as they propagate. Pinhole imaging is a typical example of this condition.
  * ** Inhomogeneous medium:** The refractive index varies with position, causing light rays to bend. Mirages are optical phenomena caused by spatial variations in the refractive index of the atmosphere.

**Mirage (inferior mirage)**\\
An inferior mirage demonstrates how a thermally stratified atmosphere alters the trajectories of light rays. The observer perceives an inverted virtual image below the real object.\\
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  * (a): Reference path, showing the straight-line propagation of light in a homogeneous medium.
  * (b): Actual upward-curved ray path through the thermally stratified, inhomogeneous atmosphere near the heated desert surface.
  * (c): Perceived line of sight. The human visual system assumes that light travels in straight lines and traces the incoming rays backward along a straight line. This extrapolation produces an inverted virtual image below the real object.

Path (c) does not represent actual light propagation; it represents the brain's geometric inference about the apparent position of the object.

**Pinhole Imaging**\\
Pinhole imaging, as demonstrated by a camera obscura, is a classic example of the rectilinear propagation of light.
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A small pinhole is made in one wall of an otherwise light-tight box. Most of the light emitted or reflected by objects outside the box is blocked by the walls; only a small fraction of the rays travelling along suitable straight paths can pass through the pinhole and enter the box.

Because light travels in straight lines, rays from different points on the object pass through the same pinhole and continue in straight lines, forming a real image on the opposite inner wall of the box. The image is inverted both vertically and horizontally.

Image quality depends on the size of the pinhole. A smaller aperture generally produces a sharper but dimmer image, whereas a larger aperture allows rays from different points to overlap, making the image brighter but more blurred.