Question

The principal section of a glass prism is an isosceles triangle ABC with AB=AC. The face AC is silvered. A ray of light is incident normally on the face AB and after two reflections, it emerges from the base BC perpendicular to the base. Angle BAC of the prism is :

Need clear explanation..

Answer 1

Answer:

let first angle of incidence

I=90°- (90-a)=a

and alpha=90°-2i=90°-2a

the second time angel of incidence

I=90°-alpha=90°-(90°-2a)=2a

beta=90°-i=90°-2a

from geometry as given in the question

a+2a+2a=180°

5a=180°

a=180°/5

a=36°

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Answer 2

Explanation:

To Find :

Angle BAC of the prism is :

Solution :

From the figure,

i₁ = 90° - (90° - A) = A

α = 90° - 2i₁ = 90° - 2A

i₂ = 90° - α = 90° - (90° - 2A) = 2A

β = 90° - i₂ = 90° - 2A

From the geometry of the figure

A + A + 2A = 180°

5A = 180°

A = 36°

Result :

Angle BAC of the prism is : 36°