A block of cubic zirconia is placed in water (n = 1.33). A laser beam is passed from the water through the cubic zirconia. The angle of incidence is 50 deg, and the angle of refraction is 27 degrees. What is the index of refraction of this cubic zirconia?

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Answer 1 · 2018-05-04T19:27:47

bolded text the refractive index of zirconia # a mu z#= 2.234

As the Zirconia cube is dipped in water ,the medium outside the
material is not air.

therefore the refractive index of zirconia with respect to water can

be calculated using the angles of incidence and refraction as given

in the problem. the refractive index of zirconia with respect to water

so, # w mu z # = #sin i /sin r #,

as i =angle of incidence = 50 degree

and r = angle of refraction = 27 degree

and a mu w = 1.33

therefore # w mu z# = #sin 50 /sin 27 #,

=# 0.766/ 0.454# = 1.68

We know that

#w mu z . z mu a .a mu w = 1 #

therefore

#w mu z . a mu w # = # 1 / (z mu a )# = #a mu z#

therefore #a mu z# = 1.68 . 1,33 = 2.234