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One technique for measuring the angle of a prism is shown in Figure P22.51. A parallel beam of light is

directed onto the apex of the prism so that the beam reflects from opposite faces of the prism. Show that the angular separation of the two reflected beams is given by $B=2 A$.

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here we have a prism. You light strikes at one side of prison early reflects making an angle thread up one. And this will be again that the one from the loft Reflection. Oh, this angle goes inside. And other little light, which is parallel to this one strikes here and reflects. This is normal. We call this is the two when this will be again. Is that true? We are asked to, uh, prove they're to be difficult to a. This will be angle. Okay. And B is the angle angle between a two reflected Frasier. So be real with angle from here to here, this is a would be So we are asked to prove the B is equal to to A in order to prove that there we go, right leveled angles here. This angle will be a better. And this angle, we call it dried below. Here, this angle will be own also. And if we police this back, this one, this will be from more tickle angles that the two we call this angle or delta And this angle is, um again from all this figure from this area from this area, we can write better, Better will be looking here Better will be called to 90 minus state are one. So if we just lookit here this part and this part so that our better will be 90 minus that one similarly, also will be again And 90 minor state of one. This makes all four. Is he called you a better similarly on the right inside here. So on this side of delta will be called to 90 minus 19 minus data too. And the gamma will be called to 90 minus later too. Oh then a delta will be cool to the gamma Then the whole better off Sorry be and will be. We could write it here. So this whole be from here to here saying will be will be We will be simply all for plus beta plus Gama plus Delta. We know that all far is equal to better and gamers will do. Oh, Delta. Therefore, we can very two times o r over Force Kim Then all five year um also in gamma are simply equal to the A Because they are the slopes, They're the angle slopes here, So be will be Then we called two times off a hands proved