Dispersion without Deviation

If the angles of the crown and flint glass prisms are so adjusted that the deviation produced for the mean rays by the first prism is equal and opposite to that produced by the second prism, then the final beam will be parallel to the incident beam. Such a combination of two prisms will produce dispersion of the incident beam without deviation.

Let and be the angles of the two prisms and δ and δ’ the deviation of the mean rays of light. Then



For the deviation to be zero,

δ + δ’ = 0



(The negative sign shows that the refracting angles of the two prisms are in opposite directions).

The dispersions produced by the two prisms are given by



The total dispersion (D_b – D_r) produced by the two prisms is given by





ω and ω’ are the dispersive powers of the materials of the two prisms. Fig. illustrates the case of dispersion without deviation. As the dispersive powers ω and ω’ are not equal, in such a combination there will be resultant dispersion and the final dispersed beam is parallel to the incident beam.

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