Convex and concave mirrors

Equipment

• Spherical mirror (concave/convex) with focal point and center shown in 3D
• “Incident angle” slider for the probe ray
• “Focal length” slider changing the mirror curvature
• Second ray figure highlighting the image position and special rays

Procedure

1. Identify the focal point and center of curvature

   Drag the canvas to rotate the mirror; locate the vertex, the center of curvature C and the focal point F on the principal axis. Verify on the figure that F lies halfway between the vertex and C, i.e. $f = R/2$ — a property of paraxial beams.

2. Draw the special rays and locate the image

   Adjust “Incident angle” to watch the axis-parallel ray reflect through F and the ray through F reflect parallel to the axis. Read the intersection point of the rays — the image — and check $\tfrac{1}{f} = \tfrac{1}{d} + \tfrac{1}{d'}$ with the simulated distances.

3. Vary the focal length and compare concave–convex

   Drag “Focal length” to change the curvature and see the reflected beam converge sooner or later. Infer the convex case: reflected rays diverge and only their virtual extensions meet at F behind the mirror, so the image is always virtual, upright and reduced.

Simulation

Experiment history

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