In the visible region, the dispersive powers | vedclass

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Question

(A) For two prisms combined to produce dispersion without deviation (achromatic combination), the net deviation must be zero.
Let the mean deviations

Vedclass · Accepted Answer

$d + d^{\prime} = 0$

Vedclass · Answer

(A) For two prisms combined to produce dispersion without deviation (achromatic combination), the net deviation must be zero.
Let the mean deviations produced by the two prisms be $d$ and $d^{\prime}$.
The condition for zero net deviation is given by $d + d^{\prime} = 0$.
However, the question asks for the condition of dispersion without deviation. The dispersive power $\omega$ is defined as $\omega = \frac{\delta_v - \delta_r}{\delta_y}$, where $\delta_y$ is the mean deviation $(d)$.
Thus, the angular dispersion is $	heta = \omega d$.
For the net dispersion to be non-zero while the net deviation is zero, we require $d + d^{\prime} = 0$.
Given the standard form for such problems, the condition for zero deviation is $d + d^{\prime} = 0$. If the options provided are meant to represent the relationship between dispersive powers and deviations, the correct physical condition is $d + d^{\prime} = 0$. Since the provided options seem to contain typos, the most physically relevant form for zero deviation is $d + d^{\prime} = 0$.

In the visible region, the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega^{\prime}$ and $d, d^{\prime}$ respectively. The condition for obtaining dispersion without deviation, when the two prisms are combined, is:

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