Drawing rays for a convex mirror involves understanding how light interacts with its curved surface. Convex mirrors always produce virtual, upright, and reduced images. Here's a breakdown of how to draw the key rays:
Ray Diagram Rules for Convex Mirrors
To accurately depict the image formed by a convex mirror, follow these rules for drawing ray diagrams:
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Ray 1 (Parallel Ray): A ray that travels parallel to the principal axis will reflect as if it came from the focal point (F) located behind the mirror. Draw the incident ray parallel to the axis, touching the mirror, and then draw the reflected ray diverging away from the mirror, extending a dashed line backwards through the focal point F on the other side.
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Ray 2 (Ray Aimed at the Focal Point): A ray directed towards the focal point (F) behind the mirror will reflect parallel to the principal axis. Draw an incident ray heading towards the focal point behind the mirror. When it reaches the mirror's surface, draw the reflected ray parallel to the principal axis.
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Ray 3 (Ray Aimed at the Center of Curvature): A ray directed towards the center of curvature (C) behind the mirror will reflect back along the same path. Draw an incident ray heading towards the center of curvature behind the mirror. Because it is aimed at the center of the curve, the ray hits the mirror at 90 degrees and goes straight back along its original path.
Constructing the Image
- Draw at Least Two Rays: You only need two rays to locate the image.
- Find the Intersection: The intersection point of the virtual rays (the dashed lines extended behind the mirror) determines the location of the image.
- Determine Image Characteristics: The image will be virtual (behind the mirror), upright, and smaller than the object.
Example
Imagine an object placed in front of a convex mirror:
- Ray 1: Draw a ray parallel to the principal axis from the top of the object to the mirror. Reflect it as if it originated from the focal point behind the mirror.
- Ray 2: Draw a ray from the top of the object aiming towards the focal point behind the mirror. When it reaches the mirror, reflect it parallel to the principal axis.
- Image Location: Where the dashed lines of Ray 1 and Ray 2 intersect behind the mirror, that's the top of the image. Since convex mirrors create upright images, the bottom of the image will lie on the principal axis directly below the image's top.
Key Considerations
- Convex mirrors always form virtual images. The reflected rays do not actually converge; instead, they appear to diverge from a point behind the mirror.
- The image produced by a convex mirror is always upright and reduced in size compared to the object.
- Understanding these ray diagram rules will allow you to correctly determine the image characteristics of any object placed in front of a convex mirror.
