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## geometrical optics

### 6. Series 26. Year - 3. a drowned lens

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?

Pikos went swimming

### 2. Series 25. Year - 1. rainbow

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

### 2. Series 25. Year - 2. green gnome

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

### 2. Series 25. Year - E. lenses

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.)

### 1. Series 24. Year - 2. sister planet

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?

Po hvězdných dálavách zatoužil Karel

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