Two mirrors are inclined at each other such that a ray of light incident on the 1st mirror and parallel to the 2nd mirror is reflected from the 2nd parallel to the 1st mirror.Determine the angle between the mirrors and the deviation suffered by the incident ray.
To determine the angle between the mirrors and the deviation suffered by the incident ray, we need to use the laws of reflection and geometry.
Let's denote the angle between the mirrors as θ and the deviation suffered by the incident ray as δ.
Based on the given information, we know that the incident ray is parallel to the second mirror. According to the law of reflection, the angle of incidence (i) is equal to the angle of reflection (r) for each reflection.
Now, let's break down the problem step by step:
Step 1: Reflection from the first mirror
When the incident ray hits the first mirror, it reflects back at an angle equal to the angle of incidence (i). This reflected ray becomes the incident ray for the second mirror.
Since the second mirror is parallel to the first one, the angle between the first mirror and the reflected ray is also i.
Step 2: Reflection from the second mirror
The incident ray on the second mirror is parallel to the mirror's surface. Therefore, the angle of incidence (i) is 0 degrees, and the reflected ray will also be parallel to the first mirror.
Step 3: Determining the deviation suffered by the incident ray
To find the deviation suffered by the incident ray, we need to compare its final direction with its original direction before the first reflection.
From step 2, we know that the reflected ray from the second mirror is parallel to the original incident ray (prior to the first reflection). Hence, there is no deviation in that direction.
Now, let's consider the deviation in the perpendicular direction (vertical direction).
If θ is the angle between the mirrors, we can see that the reflected ray from the first mirror has been displaced upwards by an amount equal to twice the angle i (due to the angle between the mirrors being 2θ). Therefore, the deviation in the vertical direction can be given as δ = 2i.
However, since i = r, we can write δ = 2r.
Since the reflected ray from the second mirror is parallel to the first mirror, we know that the angle of reflection (r) is equal to the angle between the mirrors (θ). Hence, the deviation suffered by the incident ray in the vertical direction is δ = 2θ.
To summarize:
- The angle between the mirrors is θ.
- The deviation suffered by the incident ray in the vertical direction is δ = 2θ.
Bear in mind that we assumed ideal conditions, such as lossless reflections and perfect parallelism of the mirrors, for this analysis. In real-world scenarios, minor deviations might exist due to imperfections.