Two plane mirrors are inclined at `70^@`. A ray incident on one mirror at incidence angle `theta` after reflection falls on the second mirror and is reflected from there parallel to the first mirror, The value of `theta` is

Options

A. ` 50 ^@ `
B. `45^@ `
C. `30 ^@ `
D. ` 55^@ `

Answer

A

Explanation

Reflected ray x is parallel to the base mirror BC.
In ` Delta ABC`, sum of the interior angles in 180.
` 90 - theta + 70 + 90 - phi = 180 ^@ `
` rArr theta + phi = 70 ^@......... ` (i)
Also ray x is `|| ` to the base mirror BC. so,
` 90 - phi = 70 ^@ `
` rArr phi = 20 ^@ ` ..... (ii)
From (i) & (ii) , ` theta = 50 ^@ `