\(A\) પ્રિઝમકોણ ધરાવતા પ્રિઝમ પર એકરંગી પ્રકાશ આપાત કરવામાં આવે છે.જો પ્રિઝમના દ્રવ્યનો વક્રીભવનાંક \(\mu \) છે.જો કિરણ \(AB \) બાજુ પર \(\theta \) કોણે આપાત થાય તો તે બાજુ \(AC\) માંથી નિર્ગમન ત્યારે જ પામશે કે જયારે __________.

A \(\theta < Si{n^{ - 1}}\left[ {\mu sin\left( {A - si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)
B \(\;\theta > co{s^{ - 1}}\left[ {\mu sin\left( {A + si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)
C \(\;\theta < co{s^{ - 1}}\left[ {\mu sin\left( {A + si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)
D \(\theta > Si{n^{ - 1}}\left[ {\mu sin\left( {A - si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\theta > Si{n^{ - 1}}\left[ {\mu sin\left( {A - si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)

Step-by-step Solution

Detailed explanation

When \({{\text{r}}_2} = {\text{C}},\) \(\angle {{\text{N}}_2}{\text{Rc}} = {90^o}\) Where \(C=\) critical angle As \(\sin C=\frac{1}{v}=\sin r_{2}\) Applying snell's law at \('R'\) \(\mu \,\,\sin {r_2} = 1\,\,\sin {90^o}\) ..... \((i)\) Applying snell's law at \('Q'\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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