A monochromatic light is incident from air on a refracting surface of a prism of angle $$750$$ and refractive index $$n0$$ $$=3$$ . The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of θ≤$$600$$ . The value of $$n2$$ is

Question

A monochromatic light is incident from air on a refracting surface of a prism of angle $$750$$ and refractive index $$n0$$ $$=3$$ . The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of θ≤$$600$$ . The value of $$n2$$ is

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Snell's Law at $$1st$$ surface:$$1$$×$$sin$$⁡$$60=3$$×$$sin$$⁡$$r1$$⇒$$sin$$⁡$$r1=12$$⇒$$r1=30$$∘We know, $$A=r1+r2$$⇒$$r2=45$$∘ Snell's Law at $$2$$ nd surface : $$12$$×$$3=n$$×$$sin$$⁡$$90$$∘⇒$$n2=1.5$$

Total internal reflection - Ray optics and optical instruments

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Total internal reflection - Ray optics and optical instruments

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Snell's Law at 1st surface:1×sin⁡60=3×sin⁡r1⇒sin⁡r1=12⇒r1=30∘We know, A=r1+r2⇒r2=45∘ Snell's Law at 2 nd surface : 12×3=n×sin⁡90∘⇒n2=1.5

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