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Obtain the equation for optical path of a medium of thickness d andrefractive index n. |
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Answer» Solution :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. Lighttravels 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 invacuum. 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 opticalpath d. of the medium is always greater than d. 
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