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JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments

Monochromatic light is incident on a glass prism of angle \(A\). If the refractive index of the material of the prism is \(μ\), a ray, incident at an angle \(\theta\), on the face \(AB\) would get transmitted through the face \(AC\) of the prism provided

  1. A \(\theta < Si{n^{ - 1}}\left[ {\mu sin\left( {A - si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)
  2. B \(\;\theta > co{s^{ - 1}}\left[ {\mu sin\left( {A + si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)
  3. C \(\;\theta < co{s^{ - 1}}\left[ {\mu sin\left( {A + si{n^{ - 1}}\left( {\frac{1}{\mu }} \right)} \right)} \right]\)
  4. 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 \('Q'\)…
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