Mirage Refraction
1. The problem asks to explain how a mirage happens.
2. A mirage is an optical phenomenon caused by the refraction of light rays due to temperature gradients in the air.
3. The key formula involved in refraction is Snell's Law: $$n_1 \sin \theta_1 = n_2 \sin \theta_2$$ where $n_1$ and $n_2$ are the refractive indices of two media, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction respectively.
4. In the case of a mirage, the air near the ground is much hotter than the air above it, causing a gradient in air density and thus refractive index.
5. Light rays traveling from cooler to hotter air bend away from the normal, curving upward.
6. This bending causes light from the sky or distant objects to be refracted towards the observer's eye, creating the illusion of water or a reflective surface on the ground.
7. Therefore, a mirage is a result of light refraction through layers of air with varying temperatures, bending light rays to produce displaced or inverted images.
This explanation covers the physical cause and the role of refraction in creating mirages.