Light is incident at angle θ1 = 40.1° on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n1 = 1.30, n2 = 1.40, n3 = 1.32, and n4 = 1.45, what is the value of (a) θ5in the air and (b) θ4 in the bottom material?

Diagram to question is attached.

a) 56.87°

b) 35.26°

Explanation:

We are given:

a) To find ∅ in air, we use the expression:

Sin∅1 = Sin∅5

Let's substitute figures in the expression above.

We now have:

1.3 Sin40.1 = 1 Sin∅5

= 0.837 = Sin∅5

= Sin∅5 = 0.837

∅5 =

∅ = 56.87°

b) We use the expression:

Sin∅5=n1 Sin1= n2 Sin∅2=n3 Sin∅3=n4 Sin∅4

Since we are to look for ∅4, we have:

n4sin∅4= n_uSin∅5

= 1.45Sin∅4 = 0.837

∅ = 35.26°

0.863333

86%

hope this

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