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## wave optics

### (6 points)3. Series 32. Year - 3. heat in the Dyson sphere

What would be the diameter of a Dyson sphere that would surround a star with the luminosity of the Sun, so the temperature on the outer surface of the sphere is $t= 25 \mathrm{\C }$?. Don't consider the presence of the atmosphere in the Dyson sphere. A Dyson sphere should be a relatively thin concave structure of spherical shape surrounding the star.

Karl likes Dyson spheres.

### (3 points)3. Series 30. Year - 1. long film

You are downloading your favourite film with file size 12 GB at 10 MB ⁄ s. Assuming the signal travels along a twisted-pair wire at the speed of light and modulation spreads the transmission speed evenly, that is at 1 b ⁄ s we would have to receive 1 second of the signal to acquire 1 bit of information, determine the length of cable filled by the film's data if it travels along a sufficiently long cable.

Michal's colleague claimed that 100Gb Ethernet frames are smaller than a chip.

### (7 points)3. Series 30. Year - 4. free radar

A red marker is placed on every bollard along a road (wavelength of the red colour used is $λ_{r}=630nm)$. When the driver of a passing car sees the marker as blue (wavelength $λ_{b}=450nm)$, she knows that she is speeding. What is the car's speed when this happens? What is the momentum and kinetic energy of a typical passenger car at this speed?

Kuba found a futuristic-looking photo on the internet.

### (5 points)2. Series 29. Year - 5. round it up

Mirek felt that during winter it is a little bit too dark for reading in his room. So he decided to make a hole in his wall for another window. He went to glass-works first to buy the glass panes. There was one nice round piece, but before he would buy it, he needed to check whether it's not too uneven (specifically convex). He placed the pane on the glass desk of the glass-works and saw rainbow circles around the centre of the pane caused by interference of the perpendicularly coming white light in the thin space between the two glasses. Mirek randomly chose two red circles ($λ≈700nm)$ and measured with a ruler their diameters $d_{k}=(10,5±0,5)\;\mathrm{mm}$ and $d_{k+1}=(13,0±0,5)\;\mathrm{mm}$. Based on these measurements he managed to determine the radius of curvature of the pane. Calculate it as well and think about it's errors.

Mirek si nechce zkazit oči.

### (8 points)6. Series 27. Year - E. gelatinous speed of light

Determine the speed of light in a translucent gelatinous cake that you will make yourself. Don't forget to describe what its composed of.

Hint: Get yourself a microwave or a laser

Karel was going through different physical websites on the internet and found http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p009.shtml

### (5 points)6. Series 27. Year - P. light according to the norms

Design a placement of lights over a table so that you will fulfill the norms for lighting. You have enough compact fluorescent lamps with a luminous flux of $P=1400lm$. Norms say that for usual work the lighting of the workplace should be $E=300lx$. The lamps can be placed into any position on the ceilling at a height of $H=2\;\mathrm{m}$ over the work desk. For simplicity's sake one can consider a square work area that has a side of $a=1\;\mathrm{m}$ a consider the lamp to be an isotropic source of light. Neglect reflection and dispersion of light.

Karel was thinking about the norms of the EU.

### (8 points)1. Series 27. Year - E. bend it but don't bend it!

Your task is to measure the spacing of a diffraction grating using the light from three different LED-diodes. In case your interested, send us an email at experiment@fykos.cz and we will send you the LED diodes, resistor, wires, and, of course, the diffraction grating. The only thing you will need to buy is a 9 V battery.

Karel spent all of our budget.

### (5 points)1. Series 26. Year - 5. Young cylinder

Consider the classical Double-slit experiment but assume that the screen behind the two slits is cylindrical. The axis of this cylinder is parallel with the the two slits and the whole apparatus is symmetrical. This axis is at a distance $L$ from the slits, radius of the cylindrical screen is $R=L⁄2$ and the separation of the two slits is $a$. Describe the diffraction pattern on the screen after it has been unrolled from the cylinder and give the locations of diffraction maxima using a coordinate corresponding to the distance on the cylinder's surface.

Terka enjoys optics.

### 6. Series 24. Year - 2. evil triangle

Let's have a long slit with a little hole next to it. Describe the interference pattern that you observe on a screen behind this aperture if you illuminate it with coherent light. You can neglect diffraction of light both due to the hole and due to the slit.