Explanation Given info: The light ray strikes the liquid surface at polarizing angle, the refracted ray then strikes the slab. The light reflected from the upper surface of the slab is completely polarized. Let θ p be the polarizing angle at which the light form air strikes the liquid surface, the angle of refraction of the light ray when it enters in the liquid is θ 2 and the angle at which it strikes the slab surface is θ 3 which must be equal to θ ′ p and the angle between the liquid and the slab is θ as shown in figure below. From the angle sum property of the triangle the sum of all the angles of the triangle is equal to 180 ° . Figure (1) From figure (2) in triangle ABD the angle θ is, θ + ( 90 ° + θ 2 ) + ( 90 − θ 3 ) = 180 ° θ = θ 3 − θ 2 (1) For air to liquid interface, the polarizing angle is tan θ p = n l n air (2) Here, n l is the refractive index of the liquid. n air is the refractive index of the air. Substitute 1.00 for n air in equation (2). tan θ p = n l n air tan θ p = ( n l 1.00 ) sin θ p cos θ p = n l (3) Form figure (1) in triangle ABD θ p = 90 ° − θ 2 (4) Substitute 90 ° − θ 2 for θ p in equation (4)

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ISBN: 8220100461262

Author: SERWAY

Publisher: Cengage Learning US

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Chapter 38, Problem 38.66AP

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The angle between the water surface and the surface of the slab as a function of n and nl

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Chapter 38, Problem 38.65AP

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The angle between the water surface and the surface of the slab as a function of n and n l

Solution Summary: The author determines the angle between the liquid surface and the surface of the slab as a function of n and _l.

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The angle between the water surface and the surface of the slab as a function of n and nl

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Chapter 38 Solutions