Obtain the equation for optical path of a medium of thickness d and refractive index n.

Explanation

Optical path of a medium is defined as the distance d. light travels in vaccum in the same time it travels a distance d in the medium.
Let us consider a medium of refractive index n and thickness d. Light travels with a speed v through the medium in a time i. Then we can write.
`v=(d)/(t),"rewritten as",t=(d)/(v)`
In the same time, light can cover a greater distance d. in vaccum as it travels with greater speed c in vacuum. Then we have,
`c=(d.)/(t),"rewritten as",t=(d.)/(c )`
As the time taken in both the cases is the same, we can equate the time t as.
`(d.)/(c)=(d)/(v)`
rewritten for the optical path d. as `d. = (c )/(v)d`
As, `(c )/(v) = n` , The optical path d. is, d. = nd
As n is always greater than I. the optical path d. of the medium is always greater than d.