To determine how many times a ray of light will reflect between two parallel mirrors before exiting, we can visualize the situation and apply some geometry. In this case, we have two mirrors, M1 and M2, each 1 meter long and separated by 1 centimeter. The ray of light strikes mirror M1 at a 45-degree angle. Let's break this down step by step.
Understanding the Setup
First, let’s clarify the arrangement:
- Both mirrors are parallel to each other.
- The distance between the mirrors is 1 cm (0.01 m).
- The length of each mirror is 1 m (100 cm).
- The ray of light hits mirror M1 at a 45-degree angle.
Analyzing the Reflections
When the ray strikes mirror M1 at a 45-degree angle, it will reflect off at the same angle due to the law of reflection, which states that the angle of incidence equals the angle of reflection. Since the mirrors are parallel, the ray will then travel towards mirror M2.
Calculating the Path
To visualize the path of the ray, we can consider the distance it travels between the two mirrors. The ray travels diagonally, and since it strikes at a 45-degree angle, the horizontal and vertical components of its path will be equal. The distance between the mirrors is 1 cm, which is the vertical distance the ray travels after each reflection.
Now, let’s calculate how far the ray travels horizontally before it exits:
- The ray travels 1 cm vertically to reach mirror M2.
- Since it’s at a 45-degree angle, it also travels 1 cm horizontally to reach the edge of mirror M2.
Counting the Reflections
Given that each mirror is 1 m long (100 cm), the ray will reflect back and forth between the mirrors until it exits. Each time it reflects, it travels 1 cm vertically and 1 cm horizontally. Therefore, the ray will reflect off mirror M2 and then return to mirror M1, continuing this pattern.
To find out how many reflections occur before the ray exits, we can calculate how many times it can travel the full length of the mirrors:
- The total horizontal distance the ray can travel before exiting is 100 cm (the length of the mirrors).
- Since it travels 1 cm horizontally for each reflection, it will reflect 100 times before it reaches the end of mirror M2.
Final Count of Reflections
However, we need to consider that the ray exits after the last reflection off mirror M2. Therefore, the total number of reflections before it exits is 100. Thus, the ray will reflect off the mirrors a total of 100 times before it finally exits from the other end of mirror M2.
In summary, the ray of light will have 100 reflections before it exits from the other end of mirror M2. This example illustrates how the geometry of light reflection works in a controlled environment with parallel mirrors.
