Ray diagrams use three predictable rays
Definition
Ray diagram
A scale drawing that uses the paths of light rays to locate and describe an image.
Definition
Principal axis
The straight line through the optical centre of a lens and its two principal foci.
- Draw the lens, the principal axis, a principal focus on each side and an upright object before drawing rays.
- Use a ruler, place arrowheads on rays and draw at least two construction rays from the top of the object.
- The image is located where refracted rays meet, or where their backward extensions meet.
A converging lens bends parallel rays through the focus
- A ray parallel to the principal axis is refracted through the principal focus on the far side of a converging lens.
- A ray through the optical centre continues undeviated.
- A ray directed through the principal focus on the near side emerges parallel to the principal axis.
- Any two of these rays are sufficient to locate the image; the third ray checks the construction.
- When refracted rays actually meet, draw the image at their intersection.
Example
Converging-lens construction
- Place the object beyond 2F2F2F on the left of a converging lens.
- Draw one ray parallel to the axis and refract it through the far focus.
- Draw a second ray through the optical centre without changing its direction.
- The rays meet between FFF and 2F2F2F on the far side, so the image is real, inverted and smaller than the object.
A diverging lens makes rays spread out
- A ray parallel to the principal axis is refracted so that it appears to have come from the principal focus on the same side as the object.
- Draw this refracted ray away from the axis, then extend it backwards with a dashed line through the near focus.
- A ray through the optical centre continues undeviated.
- The backward extensions meet on the same side as the object, between the lens and the near focus.
- A diverging lens therefore produces a virtual, upright and diminished image for a real object.
Example
Diverging-lens construction
- Draw a ray from the object top parallel to the axis, then refract it away from the axis.
- Extend the refracted ray backwards through the near focus using a dashed line.
- Draw a second ray through the optical centre.
- The backward extension meets the central ray between the lens and near focus, which locates the virtual image.
Object position changes a converging-lens image
- With the object beyond 2F2F2F, the image forms between FFF and 2F2F2F and is real, inverted and diminished.
- With the object at 2F2F2F, the image forms at 2F2F2F and is real, inverted and the same size.
- With the object between FFF and 2F2F2F, the image forms beyond 2F2F2F and is real, inverted and magnified.
- With the object at FFF, emerging rays are parallel and the image is effectively at infinity.
- With the object between the lens and FFF, the emerging rays diverge and their backward extensions form a virtual, upright and magnified image on the object's side.
Common Mistake
- Do not bend the ray that passes through the optical centre of a thin lens.
- Use solid lines for real light rays and dashed lines only for backward extensions used to locate a virtual image.
- Do not force rays to meet; extend them accurately and place the image where they intersect.
Exam technique
Constructing accurate diagrams
- Mark both foci at equal distances from the lens and keep the drawing to scale where distances are supplied.
- Start each construction ray at the top of the object.
- Use the intersection to state image position, then describe orientation and relative size.
Self review
- State the path of a ray parallel to the axis through a converging lens.
- State the path of a ray through the optical centre of a thin lens.
- Explain how to draw the refracted path of a parallel ray through a diverging lens.
- Describe the image formed by a converging lens when the object lies beyond 2F2F2F.
- Describe the image formed by a diverging lens.
