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Asked by sarveshvibrantacademy | 10 May, 2019, 11:21: AM
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As shown in figure , bubble in the lucite crystal is blocked by coin due to total internal reflection.
 
As we know for grazing angle of emergence,  1/sin(i) = μ ..............(1),

where i is angle of incidence for grazing angle of emergence and μ is refractive index of lucite crytal.
 
hence from eqn.(1) we have   1/sin(i) = 3/2    or   sin(i) = 2/3
 
but we have sin(i) = OB/AB  since begin mathsize 12px style angle end styleAOB = i , we get  tan begin mathsize 12px style angle end styleAOB = AB/AO = 2/√5 .............(2)
 
Hence AO = (√5/2)AB 
 
when a rupee coin is placed on lucite, AB = 1 cm, hence maximum depth AO = √5/2 cm

when a 50 paise coin is placed on lucite, AB = (3/4) cm, hence maximum depth AO = 3√5/8 cm
 
 
Answered by Thiyagarajan K | 10 May, 2019, 14:43: PM

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