1. Given data

• Wavelength of laser: $630\,\text{nm}$
  (This is not needed for finding the refracted angle here.)
• Angle of incidence: $i = 30^\circ$
• Light is going from diamond to air
• Refractive index of diamond: $n_1 = 2.42$
• Refractive index of air: $n_2 = 1$

2. Use Snell's law

$n_1 \sin i = n_2 \sin r$

Substitute the values:

$2.42 \sin 30^\circ = 1 \cdot \sin r$

Since,

$\sin 30^\circ = \frac{1}{2}$

So,

$\sin r = 2.42 \times \frac{1}{2} = 1.21$

3. Check physical possibility

But we know that for any real angle,

$\sin r \le 1$

Here,

$\sin r = 1.21 > 1$

which is impossible.

Therefore, refraction cannot occur.

4. Interpretation using critical angle

Since light is going from a denser medium (diamond) to a rarer medium (air), total internal reflection can occur.

Critical angle $c$ is given by:

$\sin c = \frac{n_2}{n_1} = \frac{1}{2.42}$

$c = \sin^{-1}(0.4132) \approx 24.4^\circ$

Given incidence angle is

$i = 30^\circ > c \approx 24.4^\circ$

So the ray undergoes total internal reflection, and refraction is not possible.

5. Evaluate options

• A: $24.41^\circ$ → This is actually the critical angle, not the angle of refraction. Incorrect.
• B: $30^\circ$ → Incorrect.
• C: Refraction is not possible → Correct.
• D: $53.4^\circ$ → Incorrect.

6. Final answer

The correct option is:

$\boxed{\text{C}}$

7. Comparison with stored correct answer

Stored correct answer: C
Derived answer: C
They match.