A ray of light travelling with a speed c leaves point 1 shown in figure and is reflected to point 2. The ray strikes the reflecting surface at a distance x from point 1. According to Fermat's principle of least time, among all possible paths between two points , the one actually taken by a ray of light is that for which the time taken is the least (In fact there are some cases in which the time taken by a ray is maximum rather than a minimum).

Under what condition is time taken least?

Options

A. `theta_(1) = theta_(2)`
B. x= l-x
C. `Y_(1) - Y_(2)`
D. all of these

Answer

A

Explanation

For least time `(dt)/(dx)= 0 implies (2x)/(sqrt(Y_(1)^(2) + x^(2))) - (2(l-x))/(sqrt((l-x)^(2) + Y_(2)^(2))) = 0 implies "sin"theta_(1) = "sin"theta_(2) implies theta_(1) = theta_(2)`