Light enters from air into a given medium at an angle of 45° with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15° from its original direction. The refractive index of the medium is:

We have light entering from air into a medium at an angle of 45° with the interface. The angle of incidence is measured from the normal to the interface, so the angle of incidence is $$i = 90° - 45° = 45°$$.

After refraction, the light is deviated by 15° from its original direction. The deviation equals the difference between the angle of incidence and the angle of refraction: $$\delta = i - r$$. Therefore $$r = i - \delta = 45° - 15° = 30°$$.

Now applying Snell's law: $$n_1 \sin i = n_2 \sin r$$, where $$n_1 = 1$$ (air). So: $$\sin 45° = n_2 \sin 30°$$ $$\frac{\sqrt{2}}{2} = n_2 \cdot \frac{1}{2}$$ $$n_2 = \sqrt{2} \approx 1.414$$

Hence, the correct answer is Option 3.