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Watchman

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Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

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Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

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Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/watchman/

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Exercise:
In searching the bottom of a pool at night a watchman shines a narrow beam of light from his flashlight pq.m above the water level onto the surface of the pool. Where does the spot of light hit the bottom of the pool measured from the wall beneath his foot if the pool is pq.m deep and the light hits the surface of the water pq.m from the watchman's feet?

Solution:
The beam's angle measured from the ray to the surface of the water is alpha' arctan leftfrac..right grad. Hence the beam hits the water at an angle of alphagrad to the optical axis. Since the refractive index of water is . according to Snelliu's Law the beam travels o the water at an angle of sin beta fracn_n_ sin alpha beta arcsin leftfracn_n_ sin alpharight .grad. Because the depth of the water is pq.m the light travels x h tan beta pq.m tan .grad pq.m in horizontal direction measured from the po of entrance o the water. From the watchmans feet that's pq.m+pq.mpqm.

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Tags	geometric, geometry, glas, index, law, light, optics, physics, ray, refraction, refractive, sin, snelliu's, snellius, tan, water, wave
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Difficulty	(2, default)
Points	2 (default)
Language	(English)
Type	Calculative / Quantity
Creator	uz
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