A white light is incident at $20^{\circ}$ on a material of silicate flint glass slab as shown. $μ_{v i o l e t} = 1.66$ and $μ_{r} = 1.6$ . For what value of $d$ will separation be $1 m m$ in red and violet rays?

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Answer 1

Here, glancing angle is given $2 0^{\circ}$
Therefore, angle of incidence is : $9 0^{\circ} - 2 0^{\circ} = 7 0^{\circ}$
$sin r_{v} = \frac{sin 7 0 ^{\circ}}{1 . 6 6} = \frac{0 . 9 3 9 7}{1 . 6 6} o r r_{v} = 34^{\circ} 30^{^{'}} sin r_{r} = \frac{sin 7 0 ^{\circ}}{1 . 6} = \frac{0 . 9 3 9 7}{1 . 6} o r r_{r} = 36^{\circ}$
Using $l = \frac{t sin ( i - r )}{cos r} l_{v} - l_{r} = d [\frac{sin ( i - r _{v} )}{c o s r _{v}} - \frac{sin ( i - r _{r} )}{c o s r _{r}}] 0.1 = d [\frac{sin 3 5 ^{\circ} 3 0 ^{^{'}}}{c o s 3 4 ^{\circ} 3 0 ^{^{'}}} - \frac{sin 3 4 ^{\circ}}{c o s 3 6 ^{\circ}}] o r 0.1 = d [\frac{0 . 5 8 0 7}{0 . 8 2 4 1} - \frac{0 . 5 5 9 2}{0 . 8 0 9 0}] = d [0.71 - 0.68] o r d = \frac{0 . 1}{0 . 0 3} = \frac{1 0}{3} c m$

Answer 2

Here, glancing angle is given

2 0^{\circ}

Therefore, angle of incidence is :

9 0^{\circ} - 2 0^{\circ} = 7 0^{\circ}

sin r_{v} = \frac{sin 7 0 ^{\circ}}{1 . 6 6} = \frac{0 . 9 3 9 7}{1 . 6 6} o r r_{v} = 34^{\circ} 30^{^{'}} sin r_{r} = \frac{sin 7 0 ^{\circ}}{1 . 6} = \frac{0 . 9 3 9 7}{1 . 6} o r r_{r} = 36^{\circ}

Using

l = \frac{t sin ( i - r )}{cos r} l_{v} - l_{r} = d [\frac{sin ( i - r _{v} )}{c o s r _{v}} - \frac{sin ( i - r _{r} )}{c o s r _{r}}] 0.1 = d [\frac{sin 3 5 ^{\circ} 3 0 ^{^{'}}}{c o s 3 4 ^{\circ} 3 0 ^{^{'}}} - \frac{sin 3 4 ^{\circ}}{c o s 3 6 ^{\circ}}] o r 0.1 = d [\frac{0 . 5 8 0 7}{0 . 8 2 4 1} - \frac{0 . 5 5 9 2}{0 . 8 0 9 0}] = d [0.71 - 0.68] o r d = \frac{0 . 1}{0 . 0 3} = \frac{1 0}{3} c m