Question

A ray is incident from a medium of refractive index \(2\) into a medium of refractive index \(1\). The critical angle is

• A. \(30^\circ\)
• B. \(60^\circ\)
• C. \(45^\circ\)
• D. \(90^\circ\)

Hint:

Critical angle exists only when light travels from a denser medium to a rarer medium. The formula is: \[ \sin C=\frac{n_2}{n_1} \] where \(n_1\gt n_2\).

Answer 1

The Correct Option is A

Step 1: Recall the formula for critical angle.
When light travels from a denser medium to a rarer medium, the critical angle \(C\) is given by
\[ \sin C=\frac{n_2}{n_1} \] where,
\[ n_1=\text{refractive index of denser medium} \] \[ n_2=\text{refractive index of rarer medium} \]

Step 2: Substitute the given values.
Here,
\[ n_1=2 \] and
\[ n_2=1 \] Therefore,
\[ \sin C=\frac{1}{2} \]

Step 3: Find the critical angle.
\[ C=\sin^{-1}\left(\frac12\right) \] \[ C=30^\circ \]

Step 4: Final conclusion.
Hence, the critical angle is
\[ \boxed{30^\circ} \]