Question

Define deviation without dispersion. Derive an expression for its essential condition and resultant deviation.

Answer 1

When two prisms of different materials and different suitable angles are combined so at to produce only deviation but no dispersion in the path of light, such combination of prisms is called deviation without dispersion.
Condition for deviation without dispersion:
Resultant dispersion = (Angular dispersion of crown glass prism) + (Angular dispersion of flint glass prism)
$0=({\mu }_v-{\mu }_r)A+({\mu }_v^{\prime }-{\mu }_r^{\prime })-A^{\prime }$
or $\frac{A}{A_1}=-\frac{{\mu }_v^{\prime }-{\mu }_r^{\prime }}{({\mu }_v-{\mu }_r)}$
(To derive following formula of resultant deviation)
$\delta =({\mu }_y-1)A+({\mu }_y^{\prime }-1)A^{\prime }$
or $\delta =({\mu }_y-1)A+[1-w/w^{\prime }]$
Where:
$w=$ (Dispersive power of crown prism)
$w^{\prime }=$ (Dispersive power of flint prism)