Light is incident normally upon one face of a prism of glass with an unknown ind

Question

Light is incident normally upon one face of a prism of glass with an unknown index of refraction. The light is totally reflected when the prism is sitting in the air. When the prism is immersed in a liquid whose index of refraction is 1.15, there is still total internal reflection, but when it is immersed in water, whose index of refraction is 1.33, there is no longer total internal reflection. What are the limits for possible values of the prism's index of refraction?

Light is incident normally upon one face of a prism of glass with an unknown index of refraction. The light is totally reflected when the prism is sitting in the air. When the prism is immersed in a liquid whose index of refraction is 1.15, there is still total internal reflection, but when it is immersed in water, whose index of refraction is 1.33, there is no longer total internal reflection. What are the limits for possible values of the prism's index of refraction?

Explanation / Answer

for internal reflection to occur the ray must travel from denser medium to rarer medium ;

form prism to air :

sin inv ( 1 / np ) = c ;

the incident angle is more thn the ciritical angle ;

45 > sin inv ( 1 / np ) ; -----------------1

from prism to liquid :

the incident angle is more thn the ciritical angle ;

45 > sin inv ( 1.15 / np ) ; ---------------2

from prsim to water :

the incident angle is less thn the ciritical angle ;

45 < sin inv ( 1.33 / np ) --------------------3

from 1 2 and 3 ,

1 / np < sin 45 ; np > 1.4142 ;

1.15 / np < sin 45 ; & np > 1.6263 ;

1.33 / np > sin 45 ; np < 1.8809

so

np > 1.6263 and np < 1.8809

1.6263 < np < 1.8809 <-----------ans   

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