 Hello friends welcome to another problem-solving session in this question. It's given that MNNR to parallel mirrors Sorry to plane mirrors Rain mirrors Appendicular to each other. So that means this angle is 90 degrees, right? This angle is 90 degrees Show that the incident ray CA is parallel to the reflected ray BD So you can see CA here is CA guys CA and BD Right. So they are parallel. We have to show that so how to approach this problem Clearly, this is related to the concepts of physics. So what is the concept of physics which we are going to use and that is angle of incidence? Angle of Incidents law of reflection isn't it angle of incidence is equal to angle of Reflection and I hope you understand what angle of incidence is So if we have a plane mirror and we draw the normal that is perpendicular at the point of incidence So what is the point of incidence in this case points of point of incidence is a At that point I have drawn a normal that is 90 degree Okay, that's a perpendicular. So if angle one angle one is the angle made by the incident ray So this ray is incident ray Okay for the first reflection and this ray here is reflected ray. So let me Reflected ray Okay, now this reflected ray goes on and is incident on The other mirror so at point B here at point B and then gets reflected again So this is the second reflected ray, which one is this one Okay, this is also if you see this is second reflected second Reflected okay, so after second reflection it comes out. We have to prove that CD or BD rather BD is Parallel to see We have to prove that to prove How do we prove? Obviously, we have to use the concepts of lines and angles and angles and property of a triangle in this case Because parallel means if somehow you prove corresponding angles to be equal or alternate angles to be equal or Go into your angles to be supplementary. Then we are done Let's try to do that. Okay, so What is what can we write we can say angle 1 is equal to angle 2 From the figure you can figure out where is angle 1 and 2 similarly angle 3 is equal to angle 4 y angle of angle of incidence is equal to angle of Reflection simple angle of reflection. This is what the physical law which you're going to use We have wrote earlier also to angle 1 is equal to angle 2 and angle 3 is equal to angle 4 now AO is perpendicular to Let's say a and let us put a name. So a b CD E. Let's say this name is this corner is E. So perpendicular to a E and Bo is perpendicular to Be why they are normals Normals to Plane mirrors and normal to plane mirrors are perpendicular to the surface of the mirror m and n Right now so Bo perpendicular right, that means quadrilateral be AO Be AO is a rectangle Why because there are three ninety degrees isn't it so or Automatically the fourth one will also become 90 degrees. Isn't it? So all are 90 degrees here. This is 90 degree This one is 90 degree. This one is 90 degree Isn't it that means what? AO and OB AO will be AO So let me write it here now so that the figure is in view So AO is perpendicular to Bo why? Perpendiculars for this could be another reason we have anyway said that AO be is a rectangle, but perpendiculars perpendicular to Perpendicular lines are perpendicular to each other anyways perpendicular to Perpendicular to each other So what I what do I mean? So let's say there are two perpendicular lines And if you draw two perpendicular perpendicular on to these perpendicular then the two perpendicular this one and this one themselves will be perpendicular to each other This is our prior knowledge, right? So now in triangle Oh So in triangle Oh AB angle 3 plus angle 2 plus 90 degrees that is angle Oh is 180 degrees by ASP By ASP Angle some property of a triangle Right, so that means angle 3 plus angle 2 is how much? 90 degrees right that means if I you know Double it that means 2 times angle 3 plus angle 2 will be 180 degrees That means 2 times angle 3 plus 2 times angle 2 is equal to 180 degrees Now 2 times angle 3 can be written as angle 3 plus angle 3 And this is angle 2 plus angle 2 is 180 degrees now that I know that angle 3 is equal to angle 4 So can't I write that angle one of the angle 3 I replace by 4 right same thing and this angle 1 plus angle Right 180 degrees that means what angle angle 3 plus 4 is what guys D B? a plus angle C a B is equal to 180 degrees Right if you see what is what does this mean? They are nothing but the co interior angles of Two lines BD and AC where AB is the transversal. Do you understand? So these are the lines one line second line and our BD or AB sorry AB is the transversal This is the case isn't it so therefore we can say since angle DBA and angle C AB or Co interior angles angles right, which are supplementary which are Supplementary and we learned in the previous lines and angles chapter that whenever that happens Then what will happen? We can say BD therefore BD is parallel to C a these are the two lines which were forming the co interior and angle with Transversal AB, right? I hope you understand is a very important result in Physics as well. So if two mutually perpendicular Mirrors are there so you can let the rays incident rays go back in the same direction If you put them in this fashion, right? So mutually perpendicular mirror and the angle You know and you're taking it on a or you're letting one of the rays in B to be incident on one of the mirrors then the second mirror will just reflect the The incident ray in the same direction Is it this is so beautiful a result? So you can just get the rays reflected back in the opposite direction if you have this configuration of Mirrors, I hope you understood this