Magnifying glasses, cameras, and human eyes──these are all devices that use convex lenses to form images. Let us understand the basic ray diagrams for lenses.
Basic Knowledge
A convex lens has an axis passing through its center, called the (optical axis), and special points on the axis called focal points. The distance from the center of the lens to a focal point is the focal length f.
The three basic rays used in diagrams:
① Light parallel to the optical axis passes through the lens and passes through the focal point.
② Light passing through the center of the lens continues to travel straight.
③ Light passing through the focal point passes through the lens and becomes parallel to the optical axis.
The intersection of these rays shows the position of the image formed on the screen.
Convex lens (a lens that is thicker in the center and thinner at the edges and converges light)
Focal point (the point where light parallel to the optical axis converges. There is one on each side of the lens)
Focal length f (the distance from the center of the lens to the focal point)
Real image (an image formed by light that actually converges and that can be projected onto a screen. It is inverted vertically and horizontally)
Virtual image (an image seen through a lens even though the light does not converge. It is upright and magnified)
Inverted and upright (upside down = inverted, same orientation = upright)
Further Exploration (Background and Significance)
The type of image formed changes depending on the distance between the object and the lens.
・Object farther than twice the focal length (a > 2f): an inverted and reduced real image → camera・human eye
・Object at twice the focal length (a = 2f): an inverted real image of the same size
・Object between the focal point and twice the focal length (f < a < 2f): an inverted and magnified real image → projector
・Object at the focal point (a = f): no image is formed (the light travels in parallel)
・Object inside the focal point (a < f): an upright and magnified virtual image → magnifying glass
Lens formula: 1/a + 1/b = 1/f ( a: object distance, b: image distance ). You do not need to memorize this in middle school, but understanding the relationship is useful.
- A convex lens is thick in the center → it converges light
- Three construction rays (parallel ray・central ray・focal ray)
- Farther than 2f → inverted, reduced real image (camera・eye)
- At 2f → inverted, same-size real image
- Between f and 2f → inverted, magnified real image (projector)
- Inside f → upright, magnified virtual image (magnifying glass)
- No image is formed at the focal point
Points to Note (Easily Confused)
① A real image can be projected onto a screen (the light is actually present), while a virtual image cannot (the light has not converged). ② Inverted means upside down and reversed left to right; upright means in the same orientation. Real images are always inverted, while virtual images are upright. ③ Even if the size of the lens is changed, the shape of the image does not change; only its brightness changes. ④ A concave lens always forms an upright, reduced virtual image (an advanced topic in middle school).
Practice
- What type of image is formed when an object is placed farther than twice the focal length?
- When viewing an object magnified through a magnifying glass, where is the object located relative to the focal point?
- How does light passing through the center of a lens travel after passing through the lens?