Which set of colours would be observed in the air under the conditions depicted in the figure?

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Accepted Answer

1. **Refractive Index and Wavelength:** According to Cauchy's relation, the refractive index ($\mu$) of a material is inversely proportional to the wavelength ($\lambda$) of light. Therefore, the refractive index is highest for violet and lowest for red ($\mu_V > \mu_R$).
2. **Critical Angle:** The critical angle ($i_c$) is related to the refractive index by $\sin(i_c) = 1/\mu$. Consequently, colors with higher refractive indices have smaller critical angles. Thus, the critical angle is smallest for violet and largest for red ($i_{cV} < i_{cR}$).
3. **Total Internal Reflection (TIR):** The problem implies a scenario where a middle wavelength (e.g., green) is incident exactly at its critical angle and grazes the surface. For colors with shorter wavelengths (Violet, Indigo, Blue), their critical angles are smaller than the angle of incidence, causing them to undergo Total Internal Reflection (TIR) back into the denser medium. 
4. **Refraction into Air:** For colors with longer wavelengths (Yellow, Orange, Red), their critical angles are larger than the angle of incidence. Therefore, they do not undergo TIR and will refract out into the air.
5. **Conclusion:** Even though the specific figure is missing, the physical principles indicate that the longer wavelengths (yellow, orange, and red) are the ones that emerge into the air under such conditions.

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