The refractive index of a medium ?x? with respect to a medium ?y? is 2/3
and the refractive index of medium ?y? with respect to medium ?z? is 4/3.
Find the refractive index of medium ?z? with respect to medium ?x?. If the
speed of light in medium ?x? is 3 ? 108 ms?1, calculate the speed of light
in medium ?y?

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Solution

Dear Student,
The refractive index of a medium (x) with respect to a medium (y) = $n_{x y} = \frac{n_{x}}{n_{y}} = \frac{2}{3} .$
The refractive index of a medium (y) with respect to a medium (z) = $n_{y z} = \frac{n_{y}}{n_{z}} = \frac{4}{3} .$
The refractive index of a medium (z) with respect to a medium (x) = $n_{z x} = \frac{n_{z}}{n_{x}} = \frac{n_{y}}{n_{x}} \times \frac{n_{z}}{n_{y}} = \frac{1}{n_{y z}} \times \frac{1}{n_{x y}} = \frac{3}{4} \times \frac{3}{2} = \frac{9}{8} .$
Regards

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Dear Student, The refractive index of a medium (x) with respect to a medium (y) = nxy=nxny=23. The refractive index of a medium (y) with respect to a medium (z) = nyz=nynz=43. The refractive index of a medium (z) with respect to a medium (x) = nzx=nznx=nynx×nzny=1nyz×1nxy=34×32=98. Regards