A reflection of a narrow beam of light incident normally on a plane mirror falls on a meter rule placed parallel to the mirror and at a distance of 75cm from it . If the mirror is rotated through 5° by what distance is the reflected beam displaced along the meter rule
When a narrow beam of light is incident normally on a plane mirror, it is reflected back along the same path.
In this case, as the incident light is normal to the mirror, there is no change in the position of the beam along the meter rule initially.
When the mirror is rotated through 5°, the reflected beam will also be rotated by the same angle.
To find the displacement along the meter rule, we can use the trigonometric relationship:
displacement = original distance x tan(angle of rotation)
Given that the original distance is 75cm and the angle of rotation is 5°, we can plug in these values to find the displacement:
displacement = 75cm x tan(5°)
Using a calculator, tan(5°) ≈ 0.0875
displacement ≈ 75cm x 0.0875
displacement ≈ 6.56 cm
The reflected beam will be displaced along the meter rule by approximately 6.56 cm.
To find the distance the reflected beam is displaced along the meter rule, we can consider the properties of a reflection off a plane mirror.
When a narrow beam of light incident normally (at a 90-degree angle) on a plane mirror, the light is reflected back along the same path in the opposite direction. This means that if the incident beam is initially falling on the meter rule, the reflected beam will be displaced in the opposite direction along the meter rule.
Given that the mirror is rotated through 5°, we need to find the distance the reflected beam is displaced along the meter rule.
To do this, we'll use trigonometry to calculate the displacement. The distance the reflected beam is displaced can be calculated using the formula:
Displacement = Distance x tan(angle)
Let's calculate the displacement.
Angle = 5°
Distance = 75 cm
Displacement = 75 cm x tan(5°)
Using a calculator, we find:
Displacement = 6.5483 cm (rounded to 4 decimal places)
Therefore, the reflected beam is displaced along the meter rule by approximately 6.5483 cm.