QQuestion
Prove that with a rectangular glass slab, incident ray and emergent ray are parallel to each other.
✓Answer
At the first surface O, the ray enters the glass slab from air and is refracted.
According to Snell’s law, ₁μ₂ = sin i / sin r
where,
- i = angle of incidence,
- r = angle of refraction,
- ₁μ₂ = refractive index of glass with respect to air.
At the second surface B, the ray emerges from the glass into air.
Again, by Snell’s law, ₂μ₁ = sin r / sin θ (where θ is the angle of emergence)
Since, ₂μ₁ = 1 / ₁μ₂
⇒ sin i / sin r = sin θ / sin r
⇒ sin i = sin θ
⇒ θ = i
Thus, the angle of emergence is equal to the angle of incidence. Therefore, the emergent ray is parallel to the incident ray. However, it is displaced sideways by a small distance called the lateral shift.
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