If a ray of light in a denser medium strikes a rarer medium at an angle of incidence i , the angles of reflection and refraction are respectively r a n d r ′ . If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of the medium is

Question

If a ray of light in a denser medium strikes a rarer medium at an angle of incidence i , the angles of reflection and refraction are respectively r a n d r ′ . If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of the medium is, sin - 1 ⁡ tan ⁡ r ′, sin - 1 ⁡ tan ⁡ r, tan - 1 ⁡ sin ⁡ i, cot - 1 ⁡ tan ⁡ i

MARKS App · Accepted Answer

We know that, I μ = sin ⁡ i sin ⁡ i ′ But r + r ′ = 90 o r ′ = 90 o - r ⇒ sin ⁡ r ′ = sin ⁡ 90 o - r sin ⁡ r ′ = cos ⁡ r ⇒ sin ⁡ r ′ = cos ⁡ i 1 μ = sin ⁡ i cos ⁡ i ⇒ 1 μ = tan ⁡ i ⇒ sin ⁡ i C = tan ⁡ i = tan ⁡ r The critical angle for the pair of media i C = sin - 1 ⁡ tan ⁡ r

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