Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown in Fig. E33.1. For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 cm long) after reflecting from the first mirror?

Question

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown in Fig. E33.1. For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 cm long) after reflecting from the first mirror?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. So two flat mirrors M one and M two are perpendicular to each other. A monochromatic laser beam hits the surface of M one at an angle theta 15.0 centimeters from the intersection of the two surfaces. After reflection from M one, the beam of light hits the surface of M two 25.0 centimeters away from the intersection, determine the angle of incidence theta. So our end goal is to determine the angle of incidence the, so we're given some multiple choice answers. Let's read them off to see what our final answer might be. A is 31.0 degrees. B is 39.0 degrees. C is 51.0 degrees and D is 59.0 degrees. OK. So first off, let us recall that the angle of reflection, let's call it theta subscript capital R is equal to the angle of incidence. And let's write it as theta subscript lowercase I is equal to theta. OK. So looking at the following figure here that the problem is given to us, let's take this figure and add to it to help us better visualize this problem. So after we take into account all the tidbits of information that are provided to us in the prom, we can add on to the problems diagram that they gave us to get the following diagram on the right. So looking at this figure on the right, the light hits the mirror M one at A which is A as this dotted line and M two which here's the mirror for M two hit it at B and then here's B. So as you can see, we have a triangle at Aib which as you can see right here, we'll highlight it and pink here is a right angle. So we can write the following statement, we can state that tangent of fire is equal to he is as we know, it's like opposite over hypotenuse or is it opposite over adjacent? Is tangent guys bird, let's remember our geometry. So tangent is opposite over adjacent. So the opposite side is 25.0 centimeters divided by the adjacent side which is 15.0 centimeters. So to solve for Phi all I have to do is take the inverse of tangent. So inverse tangent of 25.0 centimeters divided by 15.0 centimeters. So when we plug it into a calculator. We should get our value for Phi is 59 degrees, 59.0 degrees I should say. And now we can solve for the angle of incidence. So the equation to solve for the angle of incidents, let's recall that it's theta is equal to 90 degrees minus Phi. So let's plug in our known variables to solve for theta. So theta is equal to 90 degrees minus 59.0 degrees, which is the five value we just found, which is equal to 31.0 degrees. And that is our final answer. So this problem is a pretty easy one to solve. You just need to have an understanding of geometry and be able to create a diagram like the one I shared on the right to help you better visualize the problem and then be able to recognize the triangle and take it from there to solve for the correct answer for the angle of incidence. So looking at our multiple choice answers, that means the correct answer has to be the letter A 31.0 degrees. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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Key Concepts

Reflection of Light

Geometry of Plane Mirrors

Angle of Incidence