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Lens Ray Diagrams
Last Update: October 21, 2024
- Introduction
- Convex and Concave Lens Basics
- Ray Diagram Drawing Rules
- Convex and Concave Lens Ray Diagram (O>2F)
- Convex and Concave Lens Ray Diagram (O=2F)
- Convex and Concave Lens Ray Diagram (2F>O>F)
- Convex and Concave Lens Ray Diagram (O=F)
- Convex and Concave Lens Ray Diagram (O<F)
- Convex Lens Ray Diagram (O<<F)
- Convex and Concave Lens Ray Diagram (Summary)
Introduction
In this post, we introduce some key definitions relating to convex and concave lenses.
We then draw Ray Diagrams for various Object distances for symmetrical convex and concave lenses.
You can check out the following videos to learn more about lenses and Ray Diagrams:
Concave and Convex Lens Basics
Let’s use symmetrical (both sides are the same) convex and concave lenses to define some key measurements. Refer to the picture below as you read on.
Consider incident light rays hitting a lens surface.
According to Snell’s Law of Refraction ,the rays will refract inwards or outwards depending on the angles of incidence and the indices of refraction.
I show the normal lines at a and b in the biconvex lens picture below showing that the light bends towards the normal through the first boundary and then bends away from the normal at the second boundary.
Picture_Biconvex and Biconcave Lenses
The Optical Center of a lens is the point where incoming light rays pass through without being refracted.
- In a symmetrical lens the optical center is located at the geometric center of the lens.
- The Principal Axis is the horizontal line passing through the Optical Center.
- In an asymmetrical lens the optical center may not be at the geometric center.
The Focal Point F of a lens is the point where parallel (to the Principal Axis) light rays “converge” after passing through the lens.
- For Converging Lenses (Convex Lenses), parallel light rays entering the lens will converge (bend inwards) to a single Focal Point.
- For Diverging Lenses (also known as Concave Lenses), parallel light rays entering the lens will diverge (bend outwards).
- The Focal Point is traced back from these diverging rays.
- We say here that virtual rays traced back from the diverging rays, converge at the Focal Point.
- The Focal Distance f is the distance from F to the Optical Center.
- For symmetrical lenses , F and f are located on both sides, equidistant from the the Optical Center.
Ray Diagram Drawing Rules
Ray diagrams are essential for understanding how light interacts with lenses and mirrors.
They they help us understand the location and magnitude of lens images in relation to the location of their objects (the source of light; typically reflected light but could be produced light).
- Using the Principal Axis and the Centerline of a lens as effective x and y cartesian coordinates (i.e. x, y graph axes),
- An Object, the thing seen, is placed “to the left” of a lens.
- The Object is represented by an upright arrow with its base on the principal axis.
- We assume the thickness of the lens is negligible with respect to the length (Thin Lens Assumption)
- We thus draw rays to the centerline of the lens and not to the edges.
- For each point source on this Object, a ray diagram depicts a series of rays that will intersect at an Image point
- The total of all the Image points will represent the full Image of the Object that is projected by the lens.
- Each image point is located using any two of the three ray diagram rules described below.
- The projected Image will
- be upright or inverted.
- be the same size, smaller, or larger than the Object.
- An image on the opposite side of the object is considered a Real Image
- An image on the same side of the object is considered a Virtual Image
- Convex lenses project Real or Virtual Images
- Concave lenses only project Virtual Images.
Parallel Ray Rule
- Converging Lens: Any incident ray traveling parallel to the principal axis will refract through the lens and travel through the focal point on the opposite side of the lens.
- Diverging Lens: Any incident ray traveling parallel to the principal axis will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point located on the object side of the lens).
Focal Ray Rule
- Converging Lens: Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
- Diverging Lens: Any incident ray traveling towards F on the opposite side will refract through the lens and travel parallel to the principal axis.
Center Ray Rule
- An incident ray that passes through the center of the lens will continue in the same direction that it had when it entered the lens.
Using any two of the three rules above allows us to locate the Image Point from an Object Point.
Convex and Concave Lens Ray Diagrams (O>2F)
The following graphs assume we have thin and symmetrical convex and concave lenses. This allows us to draw rays to the centerpoint of the lense and not have to worry about drawing rays to the boundary edges.
Each of the image points can be found by drawing two out of the three ray types (parallel ray, center ray, focal ray) and then finding their intersection.
Picture_Case 1: Convex or Concave Lenses (Object > 2F)
For Case 1, where the Object distance is greater than 2F,
- The convex lens will produce a real , inverted image. It is smaller and closer to the lens than the object.
- The concave lens will always produce a virtual (on same side as object) and upright image
Convex and Concave Lens Ray Diagrams (O = 2F)
Picture_Case 2: Convex or Concave Lenses (Object = 2F)
For Case 2, where the Object distance is equal to 2F,
- The convex lens will produce a real , inverted image. It will be equidistant and the same size (as the object).
- The concave lens will always produce a smaller, virtual (on same side as object) and upright image.
Convex and Concave Lens Ray Diagrams (2F>O>F)
Picture_Case 3: Convex or Concave Lenses (Object between F & 2F )
For Case 3, where the Object distance is between 2F and F,
- The convex lens will produce a real , inverted image. It will be larger and further away from the lens (relative to the object).
- The concave lens will always produce a smaller, virtual (on same side as object) and upright image.
Convex and Concave Lens Ray Diagrams (O=F)
Picture_Case 4: Convex or Concave Lenses (Object = F)
For Case 4, where the Object distance is the same as F, the focal point,
- The convex lens will not produce an image.
- The concave lens will always produce a smaller, virtual (on same side as object) and upright image.
Convex and Concave Lens Ray Diagrams (O<F)
Picture_Case 5: Convex or Concave Lenses (Object < F)
For Case 5, where the Object distance is smaller than the focal point F,
- The convex lens now produces a larger Virtual Image (on the same side as the Object). The Image will be further away than the Object.
- The concave lens will always produce a smaller, virtual (on same side as object) and upright image.
Convex Lens Ray Diagram (O << F)
Picture_Case 6: Convex Lense (Object << F)
For Case 6, we moved the Object even further away from the focal point F.
The convex lens now produces a larger Virtual Image (on the same side as the Object). The Image will be further away than the Object. Compared to the Case 5 Image, the Image in Case 6 is smaller and closer to the lens.
Convex and Concave Lens Ray Diagrams (Summary)
Picture: Convex or Concave Lenses (Summary)
All the cases are summarized in the two graphs above.
- For the Convex lenses, the Image is Real for cases 1, 2, and 3. As the Object distance decreases, the Real Image increases in size and is further away from the lens.
- For the Convex lenses, there is no Image when the Object distance is equal to the Focal Point.
- For Convex lenses, the Image is Virtual for cases 5 and 6. The Images are further away from the lens and larger than the Object. The Image in case 6 is smaller and closer to the lens than the image in case 5.
- For the Concave lenses cases, the image is always Virtual, smaller, and closer to the lens than the Object. As the Object distance decreases, the Image size increases and gets closer to the lens.
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