Two glass slabs of thickness $t_{1}$ and $t_{2}$ are joined to make L shape as shown in the figure. The refractive indices of both glass slabs are same. A light ray is incident at point ‘P’ with an angle of incidence $θ$ as shown in the figure. It is assumed that refraction takes place from both the glass slabs. Then choose the correct option(s).

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Emergent ray passes from Q if $t_{1} = 2 t_{2}, θ = 45^{0} .$

Emergent ray passes below ‘Q’ if $t_{2} < t_{1}, θ = 45^{0}$

Emergent ray passes from Q if $t_{1} = 2 t_{2}, θ = 30^{0} .$

Emergent ray passes above ‘Q’ if $t_{2} > t_{1}, θ = 45^{0}$

answer is C, D.

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Detailed Solution

Optics: L-shaped Slabs Refraction

Refraction in L-Shaped Glass Slabs

Two glass slabs of thickness t₁ and t₂ are joined in an L shape. Both have the same refractive index, and a light ray is incident at point 'P' at angle θ. Refraction takes place at both slabs.

Key Points:

The lateral shift for each slab depends on its thickness and geometry.
After passing through both slabs, the emergent ray is parallel to the incident ray.
Net lateral displacement is determined by the relative thicknesses t₁ and t₂, and the incident angle θ.
If t₁ = t₂, the displacements may cancel and the emergent ray will pass through Q parallel to the incident ray.

General Conclusion:

The emergent ray after passing through both slabs is parallel to the incident ray, with a net lateral shift governed by their thicknesses and geometry.