A diverging beam of light from a point source S having...

A diverging beam of light from a point source S having divergence angle $\alpha$, falls symmetrically on a glass slab as shown. The angles of incidence of two extreme rays are equal. If the thickness of the glass slab is $\mathrm{t}$ and its refractive index is $\mu$, then the divergence angle of the emergent beam is (a) zero (b) $\alpha$ (c) $\sin ^{-1}\left(\frac{1}{\mu}\right)$ (d) $2 \sin ^{-1}\left(\frac{1}{\mu}\right)$

A diverging beam of light from a point source S having divergence angle $\alpha$, falls symmetrically on a glass slab as shown. The angles of incidence of two extreme rays are equal. If the thickness of the glass slab is $\mathrm{t}$ and its refractive index is $\mu$, then the divergence angle of the emergent beam is
(a) zero
(b) $\alpha$
(c) $\sin ^{-1}\left(\frac{1}{\mu}\right)$
(d) $2 \sin ^{-1}\left(\frac{1}{\mu}\right)$

Key Concepts

Beam Divergence

Beam divergence refers to the spread of a light beam as it propagates outward from a source. It quantifies the angular extent of the beam and is a crucial concept in understanding how beams evolve and interact with optical systems. The divergence angle represents the difference in direction between the extreme rays of the beam.

Refraction Through a Slab

When a diverging beam of light enters and then exits a plane-parallel slab, each ray undergoes refraction at both interfaces. Since the surfaces are parallel, the angular change induced at the first interface is exactly countered by the second interface, resulting in the emergent beam having the same divergence as the incident beam, aside from a lateral displacement.

Snell's Law

Snell's law describes the relationship between the angles of incidence and refraction when light passes from one medium to another with a different refractive index. It is expressed as sin(??) = n?/n? * sin(??), and it is fundamental in predicting how light rays bend at interfaces.

Plane-Parallel Slab

A plane-parallel slab is an optical medium bounded by two faces that are parallel to each other. When light traverses such a slab, although it experiences a lateral displacement due to the thickness of the material, its overall propagation direction remains unchanged upon emerging. This is because the refraction at the first interface is reversed at the second interface, preserving the beam's original angular disposition.

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