Path of a ray of light between two mirrors is shown in the diagram. If the length of each mirror is '$l$', what is the total path length of the ray between the mirrors?
To determine the total path length of the ray between the two mirrors, we will analyze the geometry involved. The diagram shows multiple reflections of the ray of light at a specific angle.
The essential aspect of this problem involves understanding the behavior of the light ray as it reflects between two mirrors. The length of each mirror is represented as \(l\).
- The pattern of the reflections can be visualized as a series of straight line segments forming a zigzag pattern.
- Each segment of the zigzag pattern in the horizontal direction contributes to the path length.
- From basic trigonometry, when a light ray strikes mirrors at \(30^\circ\), the effective path covered on the horizontal plane is twice the length of one complete segment of the zigzag pattern.
- In this particular setup, the ray covers a horizontal distance equal to \(2l\), considering the extend of reflections evident from the diagram.
Thus, the total path length of the ray between the mirrors, considering the geometry and the reflections, is \(2l\). This matches the given correct answer.
Conclusion: The total path length of the ray between the mirrors is \(2l\).
Important Questions from Geometry (Notes)
- Which of the following is not true for a parallelogram?
- A 6 cm long chord of a circle is at a distance of 4 cm from the centre of the circle. Find the distance of 8 cm long chord of the same circle from the centre.
- In a triangle PQR, if $\angle P + \angle R = 150^\circ$ and $\angle P + 3\angle Q = 170^\circ$, then $\angle P$ is equal to :
- PQR is a triangle. The bisectors of the internal angle $\angle Q$ and external angle $\angle R$ intersect at M. If $\angle QMR = 40^\circ$, then $\angle P$ is :
- Find the sum of 8 exterior angles of a 24-sided regular polygon.
