1. Find the refractive index of the medium

Given dielectric constant of the medium: $\varepsilon_r = 4$ and relative permeability: $\mu_r = 1$

The refractive index is $n = \sqrt{\varepsilon_r \mu_r} = \sqrt{4 \cdot 1} = 2$

So, light is travelling from a medium of refractive index $2$ to air of refractive index $1$.

2. Condition for total internal reflection

For total internal reflection, the angle of incidence must be greater than or equal to the critical angle. The critical angle $C$ is given by $\sin C = \frac{n_2}{n_1} = \frac{1}{2}$ where

• $n_1 = 2$ (denser medium)
• $n_2 = 1$ (air)

Thus, $C = \sin^{-1}\left(\frac{1}{2}\right) = 30^\circ$

3. Interpret the phrase "total intensity of incident wave will be reflected back"

This means the entire incident light is reflected, i.e. total internal reflection occurs. Hence the angle of incidence must be greater than the critical angle: $i > 30^\circ$

4. Check the options

• A: $10^\circ$ $< 30^\circ$ → not possible
• B: $20^\circ$ $< 30^\circ$ → not possible
• C: $30^\circ$ = critical angle, refracted ray grazes the interface; not total internal reflection
• D: $60^\circ$ $> 30^\circ$ → total internal reflection occurs

5. Final answer

Therefore, the correct option is: $\boxed{60^\circ}$