NCERT Physics Class 12 Exemplar Ch 9 Ray Optics and Optical Instruments Part 5
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Long Answer
Q 28 Show that for a material with refractive index , light incident at any angle shall be guided along a length perpendicular to the incident face.
Ans:
Any ray entering at an angle i shall be guided along AC if the angle the ray makes with the face is greater than the critical angle.
Or,
i.e.
Since
Or,
The smallest angle f shall be when If that is greater than the critical angle then all other angles of incidence shall be more than the critical angle.
Thus
Or,
Q 29. The mixture a pure liquid and a solution in a long vertical column (i.e, horizontal dimensions vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance, the height of the column.
Ans:

Consider a portion of a ray between x and inside the liquid. Let the angle of incidence at x be and let it enter the thin column at height y.

Because of the bending it shall emerge at with an angle and at a height From Snell’s law
Or,
Or
But