The reflection of a narrow beam of light incident normally on a plane mirror falls on a metre rule parallel to the mirror and to the distance of 1m calculate the angle of rotation of the mirror of the reflected beam is displayed 20cm along the metre rule when the mirror is rotated
To calculate the angle of rotation of the mirror, we can use the concept of similar triangles.
Let's say the angle of rotation of the mirror is θ.
When the mirror is rotated, the reflected beam travels a distance of 20 cm along the meter rule. Since the mirror and meter rule are parallel, we can consider the triangle formed by the incident beam, the reflected beam, and the distance traveled along the meter rule.
Let "d" be the distance traveled by the reflected beam along the meter rule. d = 20 cm = 0.2 m.
As the incident beam is normal to the mirror, the angle of incidence is 90 degrees. Since the incident ray, reflected ray, and the normal to the mirror at the point of incidence are all in the same plane, the angle of reflection is also 90 degrees.
In this triangle, the opposite side (20 cm) corresponds to the side opposite to the angle of rotation (θ), and the adjacent side (1 m) corresponds to the distance along the meter rule (d).
Using the tangent function: tan(θ) = opposite/adjacent = 0.2 m / 1 m = 0.2.
Taking the inverse tangent (arctan) of both sides: θ = arctan(0.2).
Using a calculator, we find: θ = 11.31 degrees (approximately).
Therefore, the angle of rotation of the mirror is approximately 11.31 degrees.