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geometrical optics

6. Series 23. Year - E. the drop

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?

5. Series 22. Year - 2. battle of Britain

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?

na schůzku donesl Honza Jelínek

5. Series 22. Year - 4. internet

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 $d$.

na schůzku donesl Honza Jelínek

4. Series 22. Year - 1. Cyclops mirror

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.

Při pohledu do zrcadla uviděl Mára.

2. Series 22. Year - 1. rainbow

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

na schůzce vypotil Aleš

1. Series 22. Year - 4. something for motorists

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.

Při cestě na soustředění zažil Marek Scholz.

4. Series 21. Year - 4. save the kidney

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.

K oprášení znalostí a dovedností z geometrie zadal Pavel Brom.

6. Series 20. Year - 2. strange atmosphere

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.

Nepoužitá úloha z archivu.

4. Series 20. Year - 2. plum wine in china


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.

Vymyslel Honza po několikáté návštěvě zmíněné restaurace.

6. Series 19. Year - 4. Sun reflection

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.

Našel Matouš v sovětské sbírce.

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