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Q32:
Write laws of refraction. Explain the same with the help of ray diagram, when a ray of light passes through a rectangular glass slab.

Solution :

1. Laws of Refraction

The phenomenon of refraction is governed by two fundamental laws which dictate the behavior of light as it transitions between two media of differing optical densities:

  • First Law (The Law of Planes): The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence all lie in the same plane. [Per Snell’s Law of Refraction geometry].
  • Second Law (Snell's Law): The ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is constant for a given pair of media and for light of a given wavelength. This constant is known as the refractive index ($\mu$ or $n$). Mathematically:
    $\frac{\sin(i)}{\sin(r)} = n_{21} = \frac{v_1}{v_2}$
    where $v_1$ and $v_2$ represent the velocity of light in the first and second media, respectively.

2. Refraction through a Rectangular Glass Slab

When light passes through a rectangular glass slab (a denser medium bounded by two parallel air-glass interfaces), it undergoes two successive refractions:

  1. First Interface (Air to Glass): The light ray bends towards the normal because it moves from a rarer medium to a denser medium ($v_{glass} < v_{air}$).
  2. Second Interface (Glass to Air): The light ray bends away from the normal because it enters a rarer medium. Because the opposite sides of a rectangular slab are parallel, the angle of emergence ($e$) equals the angle of incidence ($i$).
  3. Lateral Displacement: The perpendicular distance between the original path of the incident ray and the emergent ray is defined as lateral displacement.

3. Visual Representation

Incident Ray Emergent Ray i e

4. Summary of Observations

Phenomenon Result
Angle of Incidence ($i$) vs Emergence ($e$) $i = e$ (Due to parallel interfaces)
Lateral Displacement ($d$) Depends on the thickness of the slab and the angle of incidence.

Final Solution: The refraction of light through a rectangular glass slab results in a parallel shift of the light ray, where the emergent ray is parallel to the incident ray but laterally displaced, governed strictly by the constants defined in Snell's Law.


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