For a symmetric (equilateral) prism, the prism formula can be written as

For a symmetric (equilateral) prism, the prism formula can be written as
  1. $2 \sin \left(30+\frac{\delta m}{2}\right)$
  2. $\frac{2}{\sqrt{3}} \sin \left(30+\frac{\delta \mathrm{m}}{2}\right)$
  3. $2 \sin \left(60+\frac{\delta \mathrm{m}}{2}\right)$
  4. $\frac{2}{\sqrt{3}} \sin \left(60+\frac{\delta \mathrm{m}}{2}\right)$

Solution

$\mu=\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
For symmetric prism, $\mathrm{A}=60^{\circ}$ $\begin{aligned} \therefore \quad \mu & =\frac{\sin \left(30+\frac{\delta \mathrm{m}}{2}\right)}{\sin 30} \\ & =2 \sin \left(30+\frac{\delta \mathrm{m}}{2}\right) \quad \ldots\left(\because \sin 30^{\circ}=\frac{1}{2}\right) \end{aligned}$ ^

Asked in: MHT CET 2024 (15 May Shift 1)

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