Q20 of 805 Page 1

A jar of height h is filled with a transparent liquid of refractive index μ. At the center of the jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when it is placed on the top surface symmetrically about the centre, the dot is invisible.

Given: -


Height of the jar is h,


Transparent liquid of refractive index μ,


There is a dot at the center of bottom surface of the jar.


The problem involves the phenomenon of Total Internal Reflection,



Formula: -


From the required condition for TIR we know that,


Sin i≥μ,


Where,


i is the incident angle,


μ is the refractive index of the medium


So, from geometry we can write as,



Where, h is the height of the jar,


R is the radius of the disc,


i is the incident angle,


So,



Using the above expressions, we can write,



⇒R2≥μ2 R2+μ2 h2


⇒R2 (1-μ2 )≥μ2 h2




Conclusion: -


The minimum radius of the Disc is,



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