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

Options

A. `30^@`
B. `36^@`
C. `60^@`
D. `60^@`

Answer

B

Explanation

From the above figure,
`i_(1)= 90^@-(90^@- A) = A`
`alpha = 90^@ - 2i_(1) = 90^@ - 24`
`i_(2)=90^@- alpha=90^@ - (90^@ -2A)=2A`
`beta = 90^@ - i_(2)= 90° - 2A`
From the geometry of the figure
`A + 2A + 2A = 180^@`
`implies 5A = 180^@`
`therefore A=36^@`