Question

A man of height 2 m stands on a straight road on a hot day. The vertical temperature in the air results in a variation of refractive index with height y as `mu =mu_(0)sqrt((1+ay))` where `mu_(0)` is the refractive index of air near the road and a=`2 xx 10^(-6)//m`. What is the actual length of the road, man is able to see
A. 2000m
B. 390m
C. infinite distance
D. None of these

Answer 1

Correct Answer - A
`mu "sin"theta = mu_(0)"sin"90^(@) = mu_(0) implies "sin"theta = (mu_(0))/(mu) = (1)/(sqrt(1+ay))`
But `(dx)/(dy) = "tan"theta implies dx = (dy) ((1)/(sqrt(ay))) implies x = (1)/(sqrt(a)) overset(2)underset(0)int (1)/(sqrt(y))dy = [2sqrt((y)/(a))]_(0)^(2) = 2000m`