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Question

A glass vessel in the shape of a triangular is filled with water, and light is incident normally on the face XY. If the refractive indices for water and glass are 4/3 and 3/2 respectively, total internal reflection will occur at the glass- air surface XY only. What is the minimum value of sinθ
1241070_8bc36fbf67d34bf9ac16fa298f035c90.png
  1. >23
  2. <23
  3. >43
  4. <43

A
<23
B
<43
C
>43
D
>23
Solution
Verified by Toppr

μ=1sinC [ where u is the refractive index (u2u1) C is critical angle ]
u2u1=1sinC

3243=1sinC

32×34=1sinC

98=1sinC

sinC=89
C=62.73° ( approx. )
Incident ray is perpendicular.
Therefore it would not show any refraction or reflection. When incident ray reaches AC.
It would make a with angle of prism 600 and with ac=180°60°+90°=30°
Angle of incidence =90°30°=60°
Since incident angle is less than critical angle.

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