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:

Angle guided AC greater than the critical

Angle Guided AC Greater Than the Critical

Angle guided AC greater than the critical

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

Portion of a ray x and x + dx inside the liquid.

Portion of a Ray X and X + Dx Inside the Liquid.

Portion of a ray x and x + dx inside the liquid.

Or,

Or

But

Consider two planes at r andr + dr.

Consider Two Planes at R Andr + Dr.

Consider two planes at r andr + dr.

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