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).

Find the time for the ray to reach from point 1 to point 2.

Options

A. `(sqrt(Y_(1)^(2) + x^(2)) + sqrt((l-x)^(2)+ Y_(2)^(2)))/(c)`
B. `(l)/(c)`
C. `(Y_(1))/(c) + (Y_(2))/(c)`
D. `(2x)/(c)`

Answer

A

Explanation

Time `t = ("distance")/("speed") = (sqrt(Y_(1)^(2) + x^(2))+ sqrt((l-x)^(2) + Y_(2)^(2)))/(c)`