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Two plane mirrors are at an angle of $\theta_{1}=50.0^{\circ}$ with each other as in the side view shown in Figure $P 22.14$ . If a horizontal ray is incident on mirror 1 , at what angle $\theta_{2}$ does the outgoing reflected ray make with the surface of mirror 2$?$

$80^{\circ}$

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Ava P.

April 12, 2021

please use diagram for explanation of questions, without diagram it is difficult to understand

we're told that the two plane mirrors on an angle fatal one of 50 degrees with one another, and, uh, we're asked to look at figure p 22.14 And it says if the horizontal rays incident on Mir one at what angle fated to does the outgoing reflected Ray make with the surface of mirrors, too? Okay, so we can use the law of reflection and geometry to find the angle of the outgoing reflected raid that it's gonna make with the surface of Mir. Two. Um, so the angle between the two mirrors they don't want is equal to 50 degrees, and the figure from geometry the angle. The incident rain makes with mere one is equal to the angle between the two years. Hence, the angle made by the incident rate on Mir one, which we call 51 is equal to ADA one, so 51 is equal to 50 degrees. So by the law of reflection, the angle of incidence is equal to the angle of reflection. So hence the angle made by the reflected Ray with mere one, which is 52 is going to be equal to 51 so we have. Fight too is equal to fly. One. Therefore, fight too is equal to a fatal one. Right. So fight, too is equal to 50 degrees with some of the interior angles of a triangle is always gonna be 180 degrees. So fatal. One plus fight to plus five three is going to be equal to 180 degrees, and we need to find +53 So we'll just write down what I just said. They don't want plus fight too. Plus 53 is equal to 180 degrees so we can solve for 53 So 53 is going to be equal to 180 degrees, minus data one minus phi, too. But fight to is equal to theta one, so this is minus two beta. One they don't want is equal to 50 so this is equal to 80 degrees. So again, finally, by the law of reflection, the angle of incidence is equal to the angle of reflection. So the angular reflected Ray makes with mere two is going to be 80 degrees. So faded, too, which is equal to 53 is equal to 80 degrees. That could be boxing as our solution. The question