Question Video: Identifying the Reflected Ray for a Given Incident Ray | Nagwa Question Video: Identifying the Reflected Ray for a Given Incident Ray | Nagwa

Question Video: Identifying the Reflected Ray for a Given Incident Ray Science • Second Year of Preparatory School

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A mirror rests on a flat surface, seen from above. A light ray reflects from the face of the mirror. A different incident ray is then reflected from the same point on the mirror. Which color arrow correctly shows the direction of the reflected ray for the new incident ray, which is shown in red?

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Video Transcript

A mirror rests on a flat surface, seen from above. A light ray reflects from the face of the mirror. A different incident ray is then reflected from the same point on the mirror. Which color arrow correctly shows the direction of the reflected ray for the new incident ray, which is shown in red?

Okay, here we have a mirror that’s represented by this solid line. This dashed line is perpendicular to the mirror, and so this line is normal to the mirror. This is really important to note because we use the normal line to define the angles that rays make when reflecting. So we have an incident ray represented by this black arrow. And the corresponding reflected ray is shown by this black arrow here. But then, we also have a new incident ray, which is shown by this red arrow. We need to think about the direction that the corresponding new reflected ray would point and decide whether that direction is shown by the blue or the purple arrow.

To figure this out, we just need to remember the law of reflection, which states that any time light reflects from a flat mirror, the angle of incidence is equal to the angle of reflection. Let’s look again at the new incident ray. We’ll mark out the angle that it makes with the normal. And we can call this the new angle of incidence. Let’s also mark out the angles that the blue and purple arrows each make with the normal.

To answer this question then, we just need to recognize which of these two angles is equal to the new angle of incidence. If this isn’t clear by just looking at the diagram, it’ll be helpful to notice that the new angle of incidence is smaller than the angle of incidence made by this black arrow. So, because of the law of reflection, we know that the new angle of reflection must be smaller than the angle of reflection made by this black arrow.

Looking at the blue arrow, we can see that it actually makes a larger angle. And therefore, the blue arrow doesn’t follow the law of reflection. The purple arrow, however, does follow the law of reflection. The purple arrow shows an angle of reflection that is equal to the angle of incidence shown by the red arrow. Therefore, we know that the purple arrow correctly shows the direction of the reflected ray for the new incident ray.

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