How to Use a Ray Diagram

You’re sitting in physics class. The clock is ticking, the teacher is droning on and on, and you’re five seconds away from slamming your head on the table. The lines and curves on the whiteboard have all blurred into a fuzzy mess. Will you ever understand these ray diagrams? Yes, you will, with the help of this article! The steps for drawing ray diagrams for both types of mirrors and lenses are explained below.

Method 1
Method 1 of 5:

Concave/Converging Mirror

  1. 1
    Recognize a concave mirror. A concave mirror will curve inward, looking like a closing parenthesis, or this: ) .
  2. 2
    Draw a ray parallel to the principal axis starting at the top of the object. This ray will begin at the very top of the object and end when it touches the mirror. Be sure to draw an arrow at the end; this is what labels your drawing as a ray.
    • The principal axis is an imaginary line passing through the center of a curved mirror that is perpendicular to the mirror's surface.
    • Use a ruler, protractor, or another straight edge when drawing rays. This will ensure all the rays are neat and that they intersect a the right place.
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  3. 3
    Construct a new ray passing through the near focal point. The ray will start at the arrow where the previously drawn ray ends. Extend it significantly by tracing along a straight edge.
    • You'll want to make this ray quite longer than the previous one. This will help you (after you've drawn more rays) to find the image. Extend it at least until it passes the object.
    • A focal point is a midpoint between the center of curvature and the vertex of a mirror. On a diagram like the one in this step, a focal point will be labeled F, the center of curvature C, and the vertex A. [1]
    • The near focal point is the one in front of the mirror. The far focal point is the one behind the mirror.
  4. 4
    Draw a third ray, starting again from the top of the object. This ray will pass through the near focal point and continue until it touches the surface of the mirror.
    • Remember to add an arrow to the end of every ray you draw.
  5. 5
    Construct a final ray. This ray will begin at the previous ray's arrow. It will travel toward the object parallel to the principal axis.
    • Make sure this ray is long as well. It should travel beyond the object.
  6. 6
    Clearly mark the point where two of your rays intersect. This point will be separate from the top of the object and the focal point.
    • This is the location of the mirror image.
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Method 2
Method 2 of 5:

Convex/Diverging Mirror

  1. 1
    Recognize a convex mirror. This mirror curves outward. It will look like a stretched-out letter C or an opening parenthesis such as this one: ( .
  2. 2
    Construct a ray that begins at the top of the object and ends at the mirror's surface. This ray must be parallel to the principal axis. Use a ruler or straight edge to ensure your ray is neat and accurate.
  3. 3
    Align your straight edge so it passes through both the arrow of the ray from the previous step and the far focal point. Draw a ray along thin path, extending it far in both directions. Use a bold line for the half of the ray in front of the mirror and a dashed line for the half behind the mirror.
    • Remember: the far focal point is the one behind the mirror.
  4. 4
    Align your straight edge with the far focal point and the object’s top. Trace a ray along this path until it reaches the mirror's surface.
  5. 5
    Draw a ray passing through the end (arrow) of the previous ray. This ray must be parallel to the principal axis. Extend this ray in both directions, using a bold line in front of the mirror and a dashed line behind the mirror. The ray's arrow should point toward the object.
  6. 6
    Clearly mark the point where two of the rays intersect. This is the location of the image.
    • The dashed parts of the rays will intersect, not the bold parts. The intersection, and therefore the image, will be found behind the mirror.
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Method 3
Method 3 of 5:

Convex Lens

  1. 1
    Recognize a convex lens. A convex lens curves outward on both sides. Its shape is similar to the middle part of a Venn diagram.
  2. 2
    Draw a ray from the top of the object through the center of the lens. The center is the point where the principal axis passes through the lens. It is marked with the letter A.
    • Extend this ray significantly. You may even want to extend it to the edge of your paper. An image in a convex lens ray diagram is usually pretty far away from the lens, so making your rays long now will save you from having to go back and lengthen them later.
  3. 3
    Draw a new ray starting at the top of the object. This ray will travel parallel to the principal axis and will end at the middle of the lens.
    • The middle of the lens is the dashed line you will see on many diagrams and problems. Be sure your ray goes all the way to this line. Otherwise, your final image will be incorrect.
  4. 4
    Construct a ray passing through the arrow of the previous ray and the far focal point. Extend this ray significantly. Continue drawing this ray until it intersects the first ray you drew.
    • If the rays do not intersect, you may have made the first ray too short. Go back and extend that one until they both intersect.
    • You may also have incorrectly drawn the parallel ray. Be sure it ends at the middle of the lens (dashed line), not the surface.
  5. 5
    Construct a ray beginning at the object’s top that passes through the near focal point. Extend it until it reaches the middle of the lens (dashed line).
    • Your ray may miss the lens entirely depending on its angle. If this is the case, use a straight edge to extend the dashed line down the middle of the lens until it and your ray intersect.
  6. 6
    Construct a final ray passing through the arrow of the previous ray. This ray must travel parallel to the principal axis. Continue it until it passes the intersection of the other two rays.
  7. 7
    Clearly mark the spot where three rays intersect. This is the location of your image.
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Method 4
Method 4 of 5:

Concave Lens

  1. 1
    Recognize a concave lens. A concave lens curves inward on both sides. It is shaped like a very thick hourglass.
  2. 2
    Draw a ray from the top of the object through the center of the lens. The center is the point where the principal axis passes through the lens. It is marked with the letter A.
  3. 3
    Construct a parallel ray. This way will begin at the top of the object and end at the middle of the lens (dashed line). Make sure this ray is parallel to the principal axis by using a straight edge.
  4. 4
    Align your straight edge so it passes through the arrow of the previous ray and the near focal point. Draw a ray along this straight edge, extending it far in both directions. Use a straight line for the part of the ray coming out of the lens and a dashed line for the part that hasn’t gone through it yet.
    • Another way to think of it is that the “back” of the ray is dashed and the “front” (by the arrow) is not. The lens is what separates the front and back.
  5. 5
    Align your straight edge so that it passes through the far focal point and the object’s top. Trace a ray along this line until it touches the middle of the lens. End it there with an arrow.
  6. 6
    Construct a final ray parallel to the principal axis. This ray must pass through the arrow of the previous ray. It will travel toward the far focal point and beyond.
    • Once again, draw the ray with a dashed line until it hits the middle of the lens. After that, finish the ray with a straight line.
  7. 7
    Clearly mark the point where three of the rays intersect. This is the image.
    • You’ll likely find the image in front of the lens and above the principal axis. The dashed parts of the rays will be the ones intersecting.
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Method 5
Method 5 of 5:

Determining Other Image Qualitites

  1. 1
    Figure out whether the image is upright or inverted. If the image lies above the principal axis on your ray diagram, it will be upright. If it is below the principal axis, the image will be inverted.
    • An inverted image will be upside down!
  2. 2
    Discover the image type. There are two types of images: real and virtual. Real images can be projected on a screen, while virtual images can not. Your ray diagram will show you whether the image is real or virtual.
    • A real image is made from converging rays, i.e. rays that come together. On a ray diagram, these will be bold/straight lines (not dashed). Real images will also be inverted, meaning they lie below the principal axis on a ray diagram.
    • A virtual image is made from diverging rays, i.e. rays that travel away from each other. On a ray diagram, these will be shown with dashed lines. Virtual images will also be upright, meaning they will be located above the principal axis on a ray diagram.
  3. 3
    Determine the image size. A ray diagram will show you whether an image of an object will appear larger than, smaller than, or the same size as the object itself.
    • If the vertical distance from the principal axis to the image is greater than the vertical distance from the principal axis to the top of the object, the image will appear larger than the object.
    • If the vertical distance from the principal axis to the image is lesser than the vertical distance from the principal axis to the top of the object, the image will appear smaller than the object.
    • If the vertical distances from the principal axis to the top of the object and from the principal axis to the image are the same, then the image will appear to be the same size as the object.
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      Tips

      • Be sure to use a ruler, protractor, or another straight edge to draw your rays. This ensures accuracy and neatness. If you try to freehand the rays, they might not all intersect.
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      • Images formed by diverging rays will be located at the intersection of dashed lines on a ray diagram. These images are virtual. Real images and formed by converging rays, which are straight lines on a ray diagram.
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      References

      1. ↑ https://www.physicsclassroom.com/class/refln/Lesson-3/The-Anatomy-of-a-Curved-Mirror

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