Describe the use of converging and diverging lenses to correct long-sightedness and short-sightedness

3.2.3 Thin Lenses – Correcting Vision Problems

What is a Thin Lens?

A thin lens is a piece of glass or plastic that is very flat on both sides. It bends (refracts) light to make a clear image. Think of it as a “light‑bending” shortcut that helps the eye focus correctly.

How Lenses Work – The Lens Formula

The relationship between the object distance \$u\$, image distance \$v\$ and focal length \$f\$ is given by:

\$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\$

Short‑Sightedness (Myopia) – The Eye’s Problem

In myopia the eye’s lens is too strong or the eyeball is too long, so light focuses in front of the retina. The result? A distant object looks blurry, but close objects are clear.

• Eye’s focal point \$> f_{eye}\$
• Need to shift focus back onto the retina

Long‑Sightedness (Hyperopia) – The Eye’s Problem

In hyperopia the eye’s lens is too weak or the eyeball is too short, so light focuses behind the retina. Close objects appear blurry, while distant objects may be clearer.

• Eye’s focal point \$< f_{eye}\$
• Need to shift focus forward onto the retina

Using Lenses to Fix Vision

👓 Converging (Convex) Lenses – These are thicker in the middle. They bring light rays together, moving the focal point forward. They are used to correct hyperopia (long‑sightedness).

🔭 Diverging (Concave) Lenses – These are thinner in the middle. They spread light rays apart, moving the focal point backward. They are used to correct myopia (short‑sightedness).

Practical Example: Reading a Book

1. Without glasses, a myopic student sees the book’s words blurry because the eye focuses too early.
2. Wearing a diverging lens (🔭) spreads the light rays, allowing the eye to focus correctly on the retina.
3. The student can read comfortably, as if the book is closer than it actually is.

Summary Table