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## wave optics

### (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.

### 5. Series 24. Year - 1. warm up

*blood sedimentation*

Given a test tube full of human blood, how long does it take for the red cells to settle at the bottom (the so called blood sedimentation)? The usual method for such a measurement is to let the blood cells settle for an hour and than to measure the height of the cells that are already at the bottom (usually about 10 mm). We are interested in an approximate calculation. You may need to use the Stoke's relation $F=6$ π η r v$ and the value of dynamical viscosity of blood plasma $η$ = 2 Ns/m²$$.

*different eyes*

Aleš was sitting in a tram and the Sun was about 60° to the left. Because he was staring at a hot blond in front of him one of his eyes was in the shadow of his nose. When the blond noticed he was staring at her he turned his eyes to the right and he found out that he saw different color shades in each of his eyes. Describe the difference between the shades he observed with his left eye compared to his right eye. Why did this happen?

archive, Aleš

### 4. Series 24. Year - P. Colors

To display a cyan blue on your monitor it has to light up both blue and red segment. If you however mix blue and red temperas you see that the resulting color is purple. Imagine that the temperas consist of small pieces and describe how does the color of a mixture of blue and red temperas depends on the size of these pieces.

Lukáš

### 3. Series 24. Year - E. Paper

Experimentally determine the dependance of transparency of a paper on the incidence angle of light.

Jakub.

### 2. Series 24. Year - E. Yin and young

Most of you have probably heard about the Young's double slit experiment. Have you, however, ever tried to reproduce this experiment and see the interference patterns for yourselves? There are also mechanical analogies to this experiment. For example you can observe the interference of two waves in water or two sound waves. Choose one or more of these experiments and measure the interference pattern. Then you can calculate the wave length and the speed of wave propagation. Photos of your apparatus will be welcomed!

eee

### 5. Series 23. Year - S. a light in the matter

- The index of refraction in a nonlinear medium varies with the intensity of light $I$ as $n=n_{1}+n_{2}I$, where $n_{1}$ and $n_{2}$ are positive constants. Describe the behaviour of a ray of light of given width passing through this medium, assuming the light intensity decreases as we go from the centre to the edges of the ray. (Qualitative description is acceptable, an analytic model and solution will obtain extra credit.)

- A slab of width $a$ consists of 2$N$ parallel neigbouring slabs (with no gaps) with alternating indices of refraction $n_{1}$ and $n_{1}$. A light wave is incident perpendicularly on the front slab. What is the effective index of refraction of this composite slab for $N→∞?$ Can you think of a physical reason why?

**Hint:** for any real matrix $A$
<p style=„text-align:center;“>
lim_{$N→∞}(I+A/N)^{N}=\exp(A)$,

where $I$ is the identity matrix and exp($A)=I+A+A^{2}/2!+A^{3}/3!+\ldots]$.