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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?

The task of this problem is to investigate optical parameters of a water drop. If you place a drop on a thin glass plate, you will get an improvised magnifying glass. Examine the focal length and maximal magnification of this $drop$ glass$ in correlation with its dimensions and compare it with the theory. Notice the optical aberrations of the drop. What will happen if you try to magnify the display of the computer?

During a Battle of Britain a strong search light were used to find enemy planes. What will be the deflection from the direct direction of light beam, assuming the linear decrease of refractive index of the atmosphere. How this deflection depends on the angle of the beam towards vertical direction?

Assume a straight optical fibre. The incoming light enters fibre at maximum angle $α$ from the axis of fibre (higher angles will not be guided by fibre). What is the minimum length of the light pulse to guarantee no overlap between 0 and 1 bit (e.g. at least for short interval the intensity of signal must be minimal or maximal). The length of fibre is $d$.

Calculate the shape of mirror, in which the Cyclops head will look like a square. Cyclops head is a sphere with the eye in the middle.

When and where on the Earth you cannot see a rainbow?

At dangerous curves and crossings you often see a convex mirror. It is distorting real picture, such as distances and velocities are unreal. Assume our distance from the mirror is $d$, distance of incoming car from the mirror is $L$, its real velocity is $v$ and mirror diameter is $R$.

Based on the image in mirror, how far do we see the car? What is its apparent speed? How different is time it enters the crossing, calculated based on data from image, compared to reality? Assume some concrete values for all parameters and evaluate, if this difference can be significant.

Interpol just found that mafia has mobile laser weapons, which are guided from control room located in mountain village Obernieredorf. Control room is in maximum distance of 50 km from the weapons (at longer distance, the signal is unreliable). From control room they observe situation in Carlsbad, where all the weapons are aimed at.

Help: the innocent inhabitants of Carlsbad to find a shape and location of continuous mirror surface, which will reflect all laser rays in direction of control room. Solve problem in 2D (in plane), or in 3D, if there is a solution. Obviously, we require a proof of functionality, as we we do not want to invest money without a reason.