To solve this problem, we need to understand the behavior of light when a mirror is rotated.$\\$When a plane mirror is rotated by a small angle $\theta,$ the reflected light beam rotates by an angle $2\theta. \\$Given:$\\$• The mirror is at a distance $x$ from the source L.$\\$• The spot of light moves a distance $y$ on the scale when the mirror is rotated.$\\$Let's analyze the geometry of the situation:$\\$• The initial path of the light beam is normal to the mirror, so it reflects back along the same path.$\\$• When the mirror is rotated by $\theta,$ the reflected beam rotates by $2\theta. \\$The movement of the spot on the scale can be related to the angle of rotation:$\\$• The distance $y$ is the arc length of the circle with radius $x$ and angle $2\theta. \\$Using the arc length formula:$\\ y = 2x \cdot \theta \\$Rearrange to solve for $\theta: \\ \theta = \frac{y}{2x} \\$Therefore, the angle $\theta$ is given by $\frac{y}{2x}. \\$This corresponds to Option 4.