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25_Chapter 22 HomeworkCH22 Reflection and Refraction of Light

25_Chapter 22 HomeworkCH22 Reflection and Refraction of Light

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Reflection and Refraction of Light 257 22.50 Applying Snell’s law to this refraction gives 2 1 sin sin glass air n n θ θ = If 1 2 2 θ θ = , this becomes ( ) 2 2 2 sin sin 2 2sin cos ss 2 gla n θ θ θ = = θ or 2 cos 2 glass n = θ Then, the angle of incidence is 1 1 1 2 1.56 2 2cos 2cos 2 2 glass n θ θ = = = 77.5 = ° 22.51 In the Figure at the right, observe that 1 90 β θ = ° − and 1 90 α θ = ° − . Thus, β α = . Similarly, on the right side of the prism, 2 90 δ θ = ° and 2 90 γ θ = ° − , giving δ γ = . Next, observe that the angle between the reflected rays is ( ) ( ) B α β γ + δ + = + , so ( ) 2 B α γ + = . Finally, observe that the left side of the prism is sloped at angle α from the vertical, and the right side is sloped at angle γ . Thus, the angle between the two sides is
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