$A$ ray of monochromatic light is incident on the plane surface of separation between two media $X$ and $Y$ with angle of incidence $i$ in medium $X$ and angle of refraction $r$ in medium $Y$. The given graph shows the relation between $\sin i$ and $\sin r$. If $V_X$ and $V_Y$ are the velocities of the ray in media $X$ and $Y$ respectively,then which of the following is true?

  • A
    $V_X = \frac{1}{\sqrt{3}} V_Y$
  • B
    $V_X = \sqrt{3} V_Y$
  • C
    Total internal reflection can happen when the light is incident in medium $X$.
  • D
    $v_X = \sqrt{3} v_Y$,where $v_X$ and $v_Y$ are frequencies of the light in medium $X$ and $Y$ respectively.

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In finding out the refractive index of a glass slab,the following observations were made through a travelling microscope: $50$ vernier scale divisions $= 49$ $MSD$; $20$ divisions on the main scale in each $cm$. For a mark on paper:
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