A parallel sides slab ABCD of refractive index $$2$$ is sandwiched between two slabs of refractive indices $$2$$ and $$3$$ as shown in the Fig. The minimum value of angle θ (in$$ $$degrees) such that the ray PQ suffers total internal reflection at both the surfaces AB and CD is

Question

A parallel sides slab ABCD of refractive index $$2$$ is sandwiched between two slabs of refractive indices $$2$$ and $$3$$ as shown in the Fig. The minimum value of angle θ (in$$ $$degrees) such that the ray PQ suffers total internal reflection at both the surfaces AB and CD is

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Refer to Fig.For total internal reflection at surface AB, angle θ must be greater than or equal to the critical angle $$i1$$ given bysin⁡$$i1=$$μ$$2$$μ$$1=22=12which$$ gives $$i1=45$$∘For total internal reflection at surface CD, angle θ must be greater than or equal to the critical angle $$i2$$ given bysin⁡$$i2=$$μ$$3$$μ$$1=32which$$ gives $$i2=60$$∘Hence, for total internal reflection at both the surfaces AB and CD, the minimum value of θ $$=$$ $$60$$°.

Total internal reflection - Ray optics and optical instruments

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A parallel sides slab ABCD of refractive index 2 is sandwiched between two slabs of refractive indices $\sqrt{2}$ and $\sqrt{3}$ as shown in the Fig. The minimum value of angle $θ$ (in degrees) such that the ray PQ suffers total internal reflection at both the surfaces AB and CD is

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Total internal reflection - Ray optics and optical instruments

Remember concepts with our Masterclasses.

A parallel sides slab ABCD of refractive index 2 is sandwiched between two slabs of refractive indices 2 and 3 as shown in the Fig. The minimum value of angle θ (in degrees) such that the ray PQ suffers total internal reflection at both the surfaces AB and CD is

Ready to Test Your Skills?

free study material

A parallel sides slab ABCD of refractive index 2 is sandwiched between two slabs of refractive indices $\sqrt{2}$ and $\sqrt{3}$ as shown in the Fig. The minimum value of angle $θ$ (in degrees) such that the ray PQ suffers total internal reflection at both the surfaces AB and CD is