A ray of light is incident on a surface of glass slab at an angle 45 ° . If the lateral shift produced per unit thickness is 1 / 3 , then the angle of refraction produced is

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Lateral shift, Y = t sin ⁡ i - r cos ⁡ r Y t = sin ⁡ i - r cos ⁡ r = sin ⁡ i cos ⁡ r - cos ⁡ i sin ⁡ r cos ⁡ r = sin ⁡ i - cos ⁡ i tan ⁡ r ⇒ 1 3 = sin ⁡ 45 o - cos ⁡ 45 o tan ⁡ r = 1 2 1 - tan ⁡ r ⇒ 2 3 = 1 - tan ⁡ r ⇒ tan ⁡ r = 1 - 2 3 ∴ r = tan - 1 ⁡ 1 - 2 3

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