The index of refraction for violet light in silica flint glass is 1.66 and that

Question

The index of refraction for violet light in silica flint glass is 1.66 and that for red light is 1.62. What is the angular dispersion of visible light passing through an equilateral prism of apex angle 60.0 degree if the angle of incidence is 47.0 degree? (See figure. The index of refraction for air is 1.00.) Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.

Explanation / Answer

According to Snell’s law -

n sin = n sin given, = 47.0°
For the refraction of violet light ( n = 1.66 ) from air to glass

So, ( 1.00 ) sin 47.0° = ( 1.66 ) sin

=> sin = ( 1.00 / 1.66 ) sin 47.0°
=> = sin ¹ [ ( 1.00 / 1.66 ) sin 47.0° ] = 26.1°

Now, for the refraction of violet light from glass to air
n sin = n sin

heree, n = 1.66, = 60 - 26.1° =33.9o , n = 1.00
=> sin = ( n / n ) sin = n sin = ( 1.66 ) sin 33.9°
… = sin ¹ [ ( 1.66 ) sin 33.9° ] = 67.8°

Again, for the refraction of red light ( n = 1.62 ) from air to glass -

=> ( 1.000 ) sin 47° = ( 1.62 ) sin

=> sin = ( 1.000 / 1.62 ) sin 47°
=> = sin ¹ [ ( 1.000 / 1.62 ) sin 47° ] = 26.8°

For the refraction of red light from glass to air -

n sin = n sin given that, n = 1.62, = 26.8°, n = 1.00
=> sin = ( n / n ) sin = n sin = ( 1.62 ) sin 26.8°
=> = sin ¹ [ ( 1.62 ) sin 26.8° ] = 47°

Therefore, = - = 67.8 - 47 = 20.8°

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