A person has `D` cm wide face and his two eyes are separated by d cm. The minimum width of a mirror required for the person to view his complete face is

Options

A. `(D+d)/(2)`
B. `(D-d)/(4)`
C. `(D+d)/(4)`
D. `(D-d)/(2)`

Answer

D

Explanation

According to ray diagram:
` H_(1)M'_(1) = (H_(1)E_(2))/(2)` & `H_(2)M'_(2) = (H_(2)E_(1))/(2)`
`H_(1)E_(2) = D - (1)/(2) (D-d) = (D+d)/(2) = H_(2)E_(1)`
`M'_(1)M'_(2) = D-H_(1)M'_(1) - H_(2)M'_(2) = D - ((D+d)/(2))`
=`(D-d)/(2)`