Watchman
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
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
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
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
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
A watchman stands beside a pool at night holding a flashlight hO above the water's surface. He directs a narrow beam of light onto the water with the beam hitting the water's surface dO away from his feet. If the pool is tO deep where will the light spot reach the bottom of the pool measured from the wall directly beneath the watchman's feet?
Solution:
The beam's angle measured from the ray to the surface of the water is alpha' arctan leftfrac..right ang. 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 ang.. 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.
A watchman stands beside a pool at night holding a flashlight hO above the water's surface. He directs a narrow beam of light onto the water with the beam hitting the water's surface dO away from his feet. If the pool is tO deep where will the light spot reach the bottom of the pool measured from the wall directly beneath the watchman's feet?
Solution:
The beam's angle measured from the ray to the surface of the water is alpha' arctan leftfrac..right ang. 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 ang.. 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.
Meta Information
Exercise:
A watchman stands beside a pool at night holding a flashlight hO above the water's surface. He directs a narrow beam of light onto the water with the beam hitting the water's surface dO away from his feet. If the pool is tO deep where will the light spot reach the bottom of the pool measured from the wall directly beneath the watchman's feet?
Solution:
The beam's angle measured from the ray to the surface of the water is alpha' arctan leftfrac..right ang. 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 ang.. 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.
A watchman stands beside a pool at night holding a flashlight hO above the water's surface. He directs a narrow beam of light onto the water with the beam hitting the water's surface dO away from his feet. If the pool is tO deep where will the light spot reach the bottom of the pool measured from the wall directly beneath the watchman's feet?
Solution:
The beam's angle measured from the ray to the surface of the water is alpha' arctan leftfrac..right ang. 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 ang.. 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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Reflexion & Brechung by uz