A ray of light falls on one of two plane mirrors placed at an angle of 90 degrees. show that the direction of the ray after two reflections is parallel to the direction of the original ray.
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To show that the direction of the ray after two reflections is parallel to the direction of the original ray, we can use the concept of the Law of Reflection.
The Law of Reflection states that the angle of incidence is equal to the angle of reflection. This means that if a ray of light strikes a mirror at an angle θ, it will be reflected at an equal angle θ on the other side of the normal to the mirror.
Now, let's consider the situation described in the question. We have a ray of light falling on one of two plane mirrors placed at an angle of 90 degrees. This implies that the two mirrors are perpendicular to each other.
When the ray of light strikes the first mirror, it will experience a reflection as per the Law of Reflection. Let's say the incident angle of the ray on the first mirror is θ. According to the Law of Reflection, the angle of reflection will also be θ.
Now, this reflected ray becomes the incident ray for the second mirror. Since the mirrors are perpendicular to each other, the incident angle on the second mirror will be 90 degrees - θ (complementary to the angle of reflection on the first mirror).
Again, using the Law of Reflection, we know that the angle of reflection on the second mirror will be 90 degrees - θ (equal to the incident angle on the second mirror).
Considering the second reflection, the ray of light changes its direction by an angle of 90 degrees - θ.
Now, let's calculate the final direction of the ray after two reflections. The total change in direction after two reflections will be:
Change in direction = θ + (90 degrees - θ)
= θ + 90 degrees - θ
= 90 degrees
As we can see, the total change in direction is 90 degrees. This indicates that the final direction of the ray after two reflections is perpendicular to its original direction. Therefore, the ray after two reflections is parallel to the direction of the original ray.
In conclusion, when a ray of light falls on one of two plane mirrors placed at an angle of 90 degrees, the direction of the ray after two reflections will be parallel to the direction of the original ray.