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A monochromatic light of wavelength 6000^ A is passed through two media A and B of thickness 10 cm and 16 cm respectively. The number of waves in A is 1 2 that of B . If the refractive index of A is 4 3 , find the refractive index of B .

Options

  1. A_B= 5 3
  2. B_B= 3 5
  3. C_B= 4 3
  4. D_B= 3 2

Correct answer

A. _B= 5 3

Step-by-step solution

The number of waves N in a medium of thickness t and refractive index for a wavelength in vacuum is given by N = t _ medium = t . Given the thickness of medium A is t_A = 10 cm and refractive index _A = 4 3 , the number of waves in A is N_A = 10 (4/3) = 40 3 . Given the thickness of medium B is t_B = 16 cm and refractive index _B , the number of waves in B is N_B = 16 _B . The problem states that N_A = 1 2 N_B , which implies N_B = 2 N_A . Substituting the expressions for N_A and N_B : 16 _B = 2 40 3 Canceling from

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