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Manipal MET2015PhysicsRay Optics

Figure shows an irregular block of material of refractive index 2 . A ray of light strikes the face A B as shown in figure. After refraction, it is incident on a spherical surface C D of radius of curvature 0.4 m and enters a medium of refractive index 1.514 to meet P Q at E . Find the distance O E upto two places of decimal.

Options

  1. A7 m
  2. B7.29 m
  3. C6.06 m
  4. D8.55 m

Correct answer

C. 6.06 m

Step-by-step solution

From Snell's law, aligned & ₁ i & = ₂ r & r= ₁ ₂ i & = 1 2 45^ & 1 2 = r & r=30^ aligned This means that the ray becomes parallel to side A D inside the slab. This implies for the second face C D, u= . Given aligned R & =0.1 m ₃ v - ₂ v & = ₃- ₂ R aligned aligned 1.514 v - 2 & = 1.514- 2 R v & = 1.514 0.4 1.514-1.414 = 1.514 0.4 0.1 v=6.056 & =6.06 ~m (upto 2 decimal places) aligned

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