A material has an index of refraction n$($x$)$ that varies with position x within its thickness. Obtain an expression in terms of co and n$($x$)$ for the transit time for radiation to pass through a thickness L$.$ If n$($x$)=$ ni$(1+$ kx$),$ where ni and k are constants, what is the relation for transit time? How does wave number $($relative to that in a vacuum$)$ vary with position within the medium?