To solve the problem, let's go through it step-by-step, keeping all necessary principles of reflection in mind.
### Step 1: Understand the geometry of reflection
According to the law of reflection, the angle of incidence is equal to the angle of reflection. Therefore, if a light ray hits a mirror at an angle of 30 degrees (angle of incidence), it will reflect back at the same angle, 30 degrees (angle of reflection).
### Step 2: Effect of rotating the mirror
When a mirror is rotated by a certain angle, the direction of the reflected ray changes. Specifically, if the mirror is rotated by an angle [tex]\( \theta \)[/tex], the reflected ray rotates by twice that angle ([tex]\( 2\theta \)[/tex]).
In this problem, the mirror is rotated by 15 degrees. Therefore, the reflected ray will rotate by:
[tex]\[ 2 \times 15^\circ = 30^\circ \][/tex]
### Step 3: Calculate the overall effect
The total angle between the initial and the new reflected ray is the difference induced by the mirror rotation. Since the reflected ray rotates 30 degrees due to the rotation of the mirror, the angle between the initial reflected ray and the rotated reflected ray is exactly 30 degrees.
### Step 4: Conclusion
We now have all the information required:
- The angle of reflection initially is 30 degrees.
- Upon rotating the mirror by 15 degrees, the reflected ray rotates by 30 degrees.
- The total angle between the initial and the rotated reflected rays is 60 degrees.
So, the angle between the initial and rotated reflected rays is 60 degrees. Thus, the correct and final answer is [tex]\( 60^\circ \)[/tex].
