Question
Define angular dispersion for a prism. Obtain its expression for a thin prism. Relate it with the refractive indices of the material of the prism for corresponding colours.
✓
Answer
i. If a polychromatic beam is incident upon a prism, the emergent beam consists of all the individual colours angularly separated. This phenomenon is known as angular dispersion for a prism.ii. For any two component colours, angular dispersion is given by,
$δ_{21} = δ_2 – δ_1$
iii. For white light, we consider two extreme colours viz., red and violet.
$\therefore δ_{VR} = δ_V – δ_R$
iv. For thin prism,
$δ = A(n – 1)$
$δ_{21} = δ_2 – δ_1$
$= A(n_2 – 1) – A(n_1 – 1) = A(n_2 – n_1)$
where $n_1$ and $n_2$ are refractive indices for the two colours.
v. For white light,
$δ_{VR} = δ_V – δ_R$
$= A(n_V – 1) – A(n_R – 1) = A(n_V – n_R).$
$δ_{21} = δ_2 – δ_1$
iii. For white light, we consider two extreme colours viz., red and violet.
$\therefore δ_{VR} = δ_V – δ_R$
iv. For thin prism,
$δ = A(n – 1)$
$δ_{21} = δ_2 – δ_1$
$= A(n_2 – 1) – A(n_1 – 1) = A(n_2 – n_1)$
where $n_1$ and $n_2$ are refractive indices for the two colours.
v. For white light,
$δ_{VR} = δ_V – δ_R$
$= A(n_V – 1) – A(n_R – 1) = A(n_V – n_R).$
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