How does tilting a mirror steer a beam?
How does tilting a mirror steer a beam?
- Choose 30° incidence and identify both angles.
- Rotate the mirror by 10° with the incoming beam fixed.
- Compare the outgoing directions before and after.
What to measure
All angles are measured from the local normal, in degrees in the controls.
The idea underneath
Specular reflection preserves the angle to the local surface normal. Rotating a mirror rotates that normal and changes the outgoing beam direction by twice the mirror rotation when the incoming direction is held fixed. The scene displays a family of parallel rays on an optical bench and the normal at their intersection. Rays are geometric paths, not the transverse oscillation of the electromagnetic field.
θᵣ=θᵢ · Δφbeam=2ΔφmirrorAll angles are measured from the local normal, in degrees in the controls.
Build the argument
- Identify the optical axis and the normal to each interface.
- Apply reflection, Snell’s law, or the paraxial lens equation according to the model.
- Check limiting cases: equal indices, object at the focal plane, or a slit much wider than the wavelength.
Worked example 1
An incident ray at 35° reflects at 35° to the normal.
Worked example 2
A 5° mirror rotation steers a fixed incoming beam by 10°.
Applications
Cameras, microscopes and fibre links combine geometric paths with wave limitations. An image can be sharp geometrically and still be limited by diffraction.
Common misconception
Angles are measured from the normal, not the surface. A virtual image is located by backward ray extensions; no rays physically converge there.
A further investigation
Choose a mirror tilt that steers the beam by 24°.
Check your understanding
Reflection angles are measured from…
- The normal
- The surface
- The camera
Explanation
The reference is the local normal. The required mirror rotation is 12°.
Model limits
Perfect plane mirror and geometric rays; no roughness, absorption or polarisation.