A light wave travelling linearly in a medium of dielectric constant $$4$$, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be :
(Given : relative permeability of medium $$\mu_r = 1$$)

We need to find the angle of incidence for total internal reflection when light travels from a medium with dielectric constant $$\varepsilon_r = 4$$ to air.

The refractive index of the medium is given by $$n = \sqrt{\varepsilon_r \cdot \mu_r} = \sqrt{4 \times 1} = 2$$. At the critical angle $$\theta_c$$, the refracted ray travels along the surface (angle of refraction = $$90°$$), so $$\sin\theta_c = \frac{n_{air}}{n_{medium}} = \frac{1}{2}$$, which gives $$\theta_c = 30°$$.

Total internal reflection occurs when the angle of incidence is greater than or equal to the critical angle. For the entire incident wave to be reflected back, the angle of incidence must exceed $$30°$$. Among the given options ($$10°$$, $$20°$$, $$30°$$, $$60°$$), only $$60°$$ is greater than the critical angle, ensuring total internal reflection.

The correct answer is Option D: $$60°$$.