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Light – Reflection and Refraction — Science STD 10 — Question

CBSE BoardEnglish MediumSTD 10ScienceLight – Reflection and Refraction1 Mark
MCQ
A ray of light from a denser medium strikes a rarer medium at an angle incidence as shown in figure. The reflected and refracted rays make an angle of $90$ with each other. The angles of reflection and refraction and $r$ and $r\ ’.$ The critical angle is​​​​​​​
  • ✓
    $\sin ^{-1}(\tan r)$
  • B
    $\sin ^{-1}(\tan i)$
  • C
    $\sin ^{-1}\left(\tan r^{-1}\right)$
  • D
    $\tan ^{-1}(\tan i)$
✓

Answer

Correct option: A.
$\sin ^{-1}(\tan r)$
According to snell's law $\mu=\frac{\sin\text{r'}}{\sin\text{i}}$
$(\text{but  i = r})=\frac{\sin(90^\circ-\text{r)}}{\sin\text{r}}$
$=\frac{\cos\text{r}}{\sin\text{r}}$
$=\frac{1}{\tan\text{r}}$
$\mu=\frac{1}{\sin\text{i}_{\text{c}}}$
$\Rightarrow\sin \text{i}_{\text{c}}=\tan\text{r}$
$\text{i}_{\text{c}}=\sin^{-1}(\tan\text{r})$

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