Question

The refractive indices of flint glass for red and violet light are $1.613$ and $1.632$ respectively. Find the angular dispersion produced by a thin prism of flint glass having refracting angle of $5^{\circ }$.

• A. ${0.081}^{\circ }$
• B. ${0.075}^{\circ }$
• C. ${0.095}^{\circ }$
• D. ${0.06}^{\circ }$

Answer 1

The correct option is C ${0.095}^{\circ }$

Given that,
Refractive index of glass for red light, ${\mu }_r=1.613$
Refractive index of glass for violet light, ${\mu }_v=1.632$
Angle of prism, $A=5^{\circ }$

Deviation for the red light is given by,
${\delta }_r=({\mu }_r-1)A$
Deviation for the violet light is,
${\delta }_v=({\mu }_v-1)A$

Thus, the angular dispersion produced is:
$\Rightarrow \Delta \theta ={\delta }_v-{\delta }_r$
or, $\Delta \theta =({\mu }_v-1)A-({\mu }_r-1)A$
$\Rightarrow \Delta \theta =({\mu }_v-{\mu }_r)A$
$\Rightarrow \Delta \theta =(1.632-1.613)\times 5^{\circ }$
$\therefore \Delta \theta =0.019\times 5={0.095}^{\circ }$

Why this question? Tip: Angular dispersion is the angular region, which contains all the deviated light components after refraction from prism.