Question

Describe how to make a ray diagram for a convex lens. A:

Answer 1

Step-by-step construction (what to draw and which rays to use)

1. Draw the principal axis: a horizontal straight line.
2. Draw the lens: a vertical line (or a double-convex shape) at the center and mark its optical center O on the principal axis.
3. Mark the focal points F on both sides of the lens at distance f from O. Also mark 2F (2f) if helpful.
4. Place the object: draw an arrow standing on the principal axis to the left of the lens at the chosen object distance.

Draw at least two of these principal rays from the top of the object:

- Ray 1 (parallel ray): Draw a ray from the object top parallel to the principal axis toward the lens. After passing through a convex (converging) lens it refracts through the focal point on the far side (i.e., it passes through the right-hand F).
- Ray 2 (central ray): Draw a ray from the object top through the optical center O. This ray passes straight through the lens undeviated (a single straight line).
- Ray 3 (focal-ray): Alternatively draw a ray from the object top toward the near-side focal point (left F). After the lens this ray emerges parallel to the principal axis.

5. Locate the image:
- If the refracted rays on the image side (right side) actually converge and meet, their intersection is the real image top (draw the image arrow from the axis to that point). The image will be inverted.
- If the refracted rays diverge, extend them backward with dashed lines to the side of the object; their backward intersection gives the virtual image top (upright). Draw the image arrow accordingly.

6. Label the image distance (di) and image height (hi). Use a scale for distances if you want a quantitative diagram.

Useful formulas and special cases
- Lens equation: 1/f = 1/do + 1/di (do = object distance, di = image distance).
- Magnification: m = hi/ho = −di/do (negative means image inverted).
- Common positions:
- Object beyond 2F: image is between F and 2F, real, inverted, smaller.
- Object at 2F: image at 2F, real, inverted, same size.
- Object between F and 2F: image beyond 2F, real, inverted, magnified.
- Object at F: refracted rays are parallel → image at infinity.
- Object inside F: image is virtual, upright, magnified, located on the same side as the object.

Tips
- Use at least two rays (three for clarity); the intersection of any two is sufficient to locate the image.
- Draw refracted rays as solid lines and any backward extensions for virtual images as dashed lines.
- Keep your drawing to scale if you need numerical confirmation with the lens equation.