A glass prism has a cross section of an isosceles triangle with ? = 53.0. A ligh

Question

A glass prism has a cross section of an isosceles triangle with ? = 53.0.

A light beam is incident at an angle of ? = 48.3 and passes through the prism parallel to the base of the triangle as shown in the figure. What is the index of refraction of the glass? (Recall that the sum of all the internal angles of a triangle is 180.)

A glass prism has a cross section of an isosceles triangle with ? = 53.0. A light beam is incident at an angle of ? = 48.3 and passes through the prism parallel to the base of the triangle as shown in the figure. What is the index of refraction of the glass? (Recall that the sum of all the internal angles of a triangle is 180.)

Explanation / Answer

as a line parallel to base cut the triangle in equal proportion, the upper portion(above the refracted ray which is parallel to the base) is also an isosceles triangle. so the angle of refraction=90-[(180-53)/2)]=26.5 degrees so if index of refraction is k, then 1*sin(theta)=k*sin(26.5) k=sin(48.3)/sin(26.5)=1.6733

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