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Homework answers / question archive / This is a conceptual questions, so don't use Snell's law or any numbers
This is a conceptual questions, so don't use Snell's law or any numbers.
Two identical prisms made of dispersive glass, are placed as shown and a narrow beam of white light enters from the left. If the prisms are in the configuration for minimum deviation for green light, draw what happens to, say , the 4 colors of red, yellow, green and blue light-all the way through both prisms. Explain the picture in words too. What happens as the distance "d" between two prisms is made very small.
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This is a conceptual questions, so don't use snell's law or any numbers.
Two identical prisms made of dispersive glass, are placed as shown and a narrow beam of white light enters from the left. If the prisms are in the configuration for minimum deviation for green light, draw what happens to, say , the 4 colors of red, yellow, green and blue light-all the way through both prisms. Explain the picture in words too. What happens as the distance "d" between two prisms is made very small.
As we know that the refractive index of a substance depends on wave length of light. With decrease in wavelength refractive index increases and hence for red light it is minimum and for violet it is maximum. The angle of deviation depends on refractive index and hence maximum for violet light and minimum for red. The different rays will go in different directions and by focusing them we can see the spectrum. The rays will be divergent and after refraction from the two surfaces will go in different directions as in the diagram.
The angle between two extreme rays is called the angle of dispersion.
After the transmission from the first prism the rays are deviating from original direction and the angle between any two colored rays is equal to the difference of their angle of deviation.
Now this diverging beam in which different rays are going in different directions incidents on the second prism at different points and in deferent directions and again gets refracted through the second prism. As the angle of incident on second prism is equal to the angle of transmission from the first (the surfaces are parallel) the angle of deviation is equal to that by the first but as the refracting angle of the second prism is opposite the deviation will be in the opposite (upward) direction the ray becomes parallel to that of initial incident ray. So all the rays will become parallel to initial composite white light ray and the beam will be a parallel beam with different colors separated transversally. If we focus them by an achromatic lens they will focus to a point and hence no colors will be seen.
This can be understood in this way as well. As the angle of dispersion ? is the angle between the emergent red and violet rays by the first prism violet ray deviates ? more then red one. As the second prism is inverted it deviates violet ray again ? more but in opposite direction and hence net deviation of violet ray relative to red is zero and both will emerge parallel from the second prism. In this way all emergent rays become parallel.
Now if the distance d between the prisms decreased the distance between the points of incident rays will decrease and hence the transverse distance between the rays will decrease. So the rays of different colors are still parallel but they will be more close to each other.