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°

peru sabe que indecopi jamas sirve imponen barreras para defender tus derechos. indecopi jamas investiga los casos a fondo y peor aun indecopi no defiende como debe ser los derechos de los consumidores. indecopi esta pintada es una institucion pagada por nuestros impuestos sin embargo nunca nos sirve para nada. indecopi jamas castiga a las operadoras ejemplarmente, encima nos cobran por reclamar lo que deberia ser gratuito y nunca investigan, pero si engordan sus bolsillos con nuestros impuestos, en conclusion indecopi esta pintada no sirve para nada.