Geometrical OpticsHard

Question

A rectangular glass slab ABCD of refractive index is immersed in water of refractive index n2 (n1 > n2). A ray of light is incident at surface AB of the slab as shown. The maximum value of the angle of incidence αmax, such that the ray comes out only from the other surface CD, is giiven by
        

Options

A.
B.
C.
D.

Solution

          
Rays come out only from CD, means rays after refraction from AB get total internally reflected at AD.
From figure
    r1 + r2 = 90o
∴   r1 = 90o - r2
      (r1)max = 90o - (r2)min and
      (r2)min = θc (For total internal reflection at AD)
Where, sin θc = or θc = sin-1
     ∴ (r1)max = 90o - θc
Now applying Snell’s law at face AB

or     sin αmax = cosθC
∴ αmax = sin-1

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