The critical angle for a denser-rarer interface is 45$$^\circ$$. The speed of light in rarer medium is $$3 \times 10^8$$ m s$$^{-1}$$. The speed of light in the denser medium is:

The critical angle $$\theta_c$$ for a denser-rarer interface is related to the refractive indices by:

$$\sin \theta_c = \frac{n_r}{n_d} = \frac{v_d}{v_r}$$

where $$v_d$$ and $$v_r$$ are the speeds of light in the denser and rarer media respectively.

We are given that $$\theta_c = 45°$$, $$v_r = 3 \times 10^8$$ m/s

$$\sin 45° = \frac{v_d}{v_r}$$

$$\frac{1}{\sqrt{2}} = \frac{v_d}{3 \times 10^8}$$

$$v_d = \frac{3 \times 10^8}{\sqrt{2}} = \frac{3 \times 10^8 \times \sqrt{2}}{2} = \frac{3 \times 1.414 \times 10^8}{2}$$

$$v_d = \frac{4.243 \times 10^8}{2} = 2.12 \times 10^8 \text{ m/s}$$

The speed of light in the denser medium is $$2.12 \times 10^8$$ m/s.