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The refractive index of atmosphere of a planet of radius $R$ is can be describe by following equation: $n=n_{0}-αh$. Calculate, how high above the surface of the planet $h$ the laser beam will follow circular trajectory around the planet.

In our popular Chinese restaurant in Prague they give to each guest with the receipt small glass of plum wine. The wine is served in small ceramic bowl with double bottom (figure 1). The top bottom is glass and you can see picture of sitting girl (figure 2). When the glass is emptied the girl disappears (figure 3). Explain what happens. The empty bowl is in figure 4.

During sunny days we often experiment with square mirror giving reflections of Sun. Sometimes the reflection has LICHOBEZNIK shape, sometimes it is elliptical shape. What are the conditions for each case to happen? If possible, formulate your condition quantitatively.

Lets have a lens of focal length $f$. The light source is at optical axis in distance $a>f$ from the lens. The light source starts moving at constant speed towards the lens. Calculate the speed of movement of the image of the light source. Decide, if this speed can be bigger than the speed of light. Would it contradict special theory of relativity?

The water sprite (unterwasermann for German speakers) is sitting 1.5 meters under water level of his pond. How he sees the world above the water level? Assume, that refractive index of eye is same as refractive index of water.