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The drawing shows a laser beam shining on a plane mirror that is perpendicular to the floor. the angle of incidence is 33.0°. the beam emerges from the laser at a point that is 1.10 m from the mirror and 1.80 m above the floor. after reflection, how far from the base of the mirror does the beam strike the floor?

Respuesta :

Demiurgos
I have attached the sketch for this problem.
The goal is to find the length d. Law of reflection tells us that angle of incidence is the same as the angle of reflection. Also, the angle between the ground and the beam that is reflected is the same as the angle of incidence.
Because all of this angles are the same we know that tangens of those angles must be the same.
[tex]tan(\theta)=\frac{x}{l}\\ tan(\theta)=\frac{h-x}{d}\\ [/tex]
From the first formula we figure out that x is:
[tex]x=l\tan(\theta)[/tex]
Now we plug that into the second one:
[tex]d\tan(\theta)=h-x; \ x=l\tan(\theta)\\ d\tan(\theta)=h-l\tan(\theta)\\ d=\frac{h}{tan(\theta)}-l[/tex]
When we plug in the number we get:
[tex]d=1.67m[/tex]


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