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Pikos' friend wears glasses. When she puts them on, her eyes seem to be smaller. Is she shortsighted or farsighted? Justify your answer.

Consider an optical system composed of three semitransparent mirrors placed behind each other along one axis. Every mirror by itself reflects half of incident light and lets the other half pass. Determine what fraction of light passes through the system of mirrors.

Bonus: Solve the problem for $n$ such mirrors.

Imagine that around the Sun on a circular orbit is a convex lens with a diameter that is equal to the diameter of the Sun, the focal point of which orbits with a sufficient precision on the orbit of Earth. Determine how the lens will burn the Earth during one of its orbit (ie. how much solar energy will be given to Earth by the lens), if it orbits at the distance of Mercury and compare it with the state where it will be as far as Venus.

Bonus: Consider the eclipse that the lens will cause during its orbit.

On the surface of water a thin biconcave lens made from a light-weight material is floating. The radii of both surfaces are $R=20\;\mathrm{cm}$. Determine the distance between the two focal points of the lens, if the index of refraction of the air above the lens is $n_{a}=1$, index of refraction of the lens is $n_{l}=1.5$ and index of refraction of water is $n_{w}=1.3$.

Bonus: Assume that it is a lens of width $T=3\;\mathrm{cm}$, and within it is symmetrically place an air bubble in the shape of a biconcave lens with the radii of curvature $r=50\;\mathrm{cm}$ and width $t=1\;\mathrm{cm}$.

Can you see the Moon from Mars with a naked eye.Ground your answer in calculations.

If an object is placed a distance $p$ from a thin glass lens (index of refraction $n_{s})$, we can see its image on a screen that is placed a distance $d$ from the lens. Without altering any distances, we immerse this system into a liquid (index of refraction $n)$. Under what conditions can we still observe the object's image on the screen, and how far from lens would this image be?

What would a rainbow look like if it was raining oil, sulfuric acid or glass instead of water?

What would you see if you were standing at one end of a rainbow?

Determine type and focal length of enclosed lenses. (If you're new to FYKOS just send as an email to <tt>cocky@fykos.cz</tt> and we will send you a set of lenses.)

Many planets outside our solar system have been discovered during the past few years. It would be much more interesting, however, if we discovered a planet similar to the Earth. Assume that you want to find an Earth-like planet (radius close to that of the Earth) which orbits a sun-like star (similar mass and radius) once per terrestrial year. Assume that this system is about 10 pc away from the Sun. Find conditions which would allow you to observe the planet only by measuring the decrease in the star's luminosity and estimate how long will this decrease last. What would you do if the system contained more than one planet?