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exercises.md

@@ -188,7 +188,9 @@ Bear in mind the main purpose of this quiz is for you to test your understanding
 85. Is political correctness and censorship ever justified?
 86. Firstly convert the expression *x + (1 + 2) / (3 - 4)* to [postfix notation](postfix.md) (also reverse Polish notation). State some major advantages of postfix notation against infix notation. Now please state disadvantage of postfix notation, especially that which would be significant if we e.g. use it for expression such as *myFunc(x,y,myFunc2(z))*.
 87. What does the [demultiplexer](demultiplexer.md) logic circuit do? Give an example of when it's used. How is it related to [multiplexer](multiplexer.md)?
-88. Did you enjoy this quiz?
+88. [Optical fiber](optical_fiber.md) cabels mustn't be bent too much -- one reason for this is that the fibers inside might crack, but another reason is related to the physics of how the light travels inside. What is this effect of optics called and why does it limit the bend radius?
+89. We know that an [ellipse](ellipse.md) is a set of points in 2D plane that have constant sum of [distances](distance.md) to some two given points that are called *focal points*. What if we instead consider a taxicab distance (computed as distance alongside X axis plus distance alongside Y axis)? Consider the constant sum of distances to always be set higher than the taxicab distance of the two focal points. What shape will we get? Just describe the shape and intuitively show why it looks like that.
+90. Did you enjoy this quiz?
 
 ### Answers
 
@@ -279,7 +281,9 @@ Bear in mind the main purpose of this quiz is for you to test your understanding
 85. no
 86. *x 1 2 + 3 4 - / +*; Advantages are for example not needing brackets at all and simple parsing and evaluation, for example we don't have to care about operator precedence. Disadvantages may be e.g. lower readability; we also have to know each operator's arity because from postfix notation it can't be deduced -- with infix notation expression *myFunc(x,y,myFunc2(z))* it is clear that *myFunc* takes 3 arguments and *myFunc2* takes 1, but if we convert it to postfix notation, we get *x y z myFunc2 myFunc3*, from which it isn't clear how many arguments each function takes.
 87. It's a circuit that on its input takes data and output address -- a number from 0 to *N - 1* -- and that sends the data to one of *N* output ports (identified by the given address). It can be imagined like a switch that redirects an input stream to one of *N* output channels. Its use may be for example to redirect input data, for example audio, to one of several output devices, for example speakers, headphones and audio recorders. Multiplexer is a circuit that does the opposite (i.e. chooses input from *N* channels that is then sent to a single output channel).
-88. yes
+88. Total internal refraction -- light travelling in the fibers bounces off of the walls of the fiber, but in order to bounce (be reflected) when it hits the boundary it must hit it under an angle that's smaller than so called critical angle which is calculated from the indices of refraction of the fiber and the material outside of it. If the cable was bent too much, light could hit the boundary under and angle close to perpendicular and by this it would escape to the outside medium.
+89. Kind of octagon but with unevenly long sides; a rectangle with bevelled corners, i.e. two horizontal sides, two vertical sides, two 45 degree walls and two 135 degree walls. We can imagine taxicab distance from given point like sort of a diamond, it creates 4 quadrants around the point, in each the distance increases linearly in diagonal direction -- regions of constant distance here form 45 degree angled squares. Boundaries between these quadrants form a cross of infinite size. Taking two different points these two crosses will overlap and form 9 regions (draw it): top-left, top-middle, top-right, middle-left etc. Examining each of the regions we will find that it either keeps the increasing direction the same (if both overlaid directions are the same) or that some principal direction cancels out and leave the sum increasing only in one principal direction -- basically we find that in each of those regions the sum increases linearly in one of 8 directions separated by 45 degrees (except for the middle region where the sum is constant). It's also clear the heightmap has to stay continuous as both of the summed functions are continuous. From all this we can deduce the shape basically.
+90. yes
 
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