A man of height H is standing in front of an inclined plane mirror at an angle `theta` from horizontal. The vertical separation between man and inclined plane is x. Man can see its complete image in length `(H(H+x)"sin"theta)/(H +2x)` of mirror .
(Given : x = H = 1m and `theta = 45^(@)`)

If man starts moving with velocity `sqrt(2)ms^(-1)` along inclined plane, find out length of mirror at t = 1s in which he can see his complete image,

Options

A. `(sqrt(2))/(3)m`
B. `(2)/(3)`
C. `(1)/(3)m`
D. `(1)/(3sqrt(2))m`

Answer

A

Explanation

In this case x, H and `theta` remains same so required length of mirror = `(H(H+x)"sin"theta")/(H + 2x)`
=`(1(1+1)"sin"45^(@))/(1 + 2 xx1) = (sqrt(2))/(3)m`