10.1.2 Defects of vision and their correction using lenses

Lenses

In vision, lenses are used to correct common vision defects by refracting light to change its direction. This section covers converging and diverging lenses and explains how they correct specific vision issues.

Types of Lenses

1. Converging Lenses (Convex):

• Curved outward, they bring parallel light rays closer together at a focal point.
• Can create both real images (which can be projected onto a screen) and virtual images (which cannot).
• Real images form when the object is farther than the focal length, and virtual images form when the object is closer than the focal length.

2. Diverging Lenses (Concave):

• Curved inward, they cause parallel rays to spread out (diverge).
• Always form virtual images as the rays appear to originate from a point behind the lens.

Key Lens Terms

• Principal Focus (F): The point where parallel rays converge (for converging lenses) or appear to diverge from (for diverging lenses).
• Focal Length (f): The distance from the lens centre to the principal focus.
• Power of Lens (P): Indicates a lens's ability to bend light. Given by the formula:

$$P = \frac{1}{f}$$

where $f$ is the focal length in metres. For converging lenses, $P$ is positive, and for diverging lenses, $P$ is negative.

Ray Diagrams for Image Formation

To locate the image produced by a lens:

3. Draw two rays from the object:

• One through the lens centre (it remains unrefracted).
• Another parallel to the principal axis, refracting through the principal focus.

4. Real images form where rays meet; virtual images form where rays appear to diverge.

Lens Formula and Magnification

1. Lens Formula:

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

Where:

• $u$ = object distance from the lens.
• $v$ = image distance from the lens.
• $f$ = focal length.

2. Magnification (m):

$$m = \frac{\text{image size}}{\text{object size}} = \frac{v}{u}$$

Common Vision Defects

1. Myopia (Short-Sightedness):

• Unable to focus on distant objects; image forms before the retina.
• Caused by an eyeball that is too long or excessive lens power.
• Corrected with diverging lenses to extend the focal point.

2. Hypermetropia (Long-Sightedness):

• Unable to focus on close objects; image forms behind the retina.
• Caused by an eyeball that is too short or insufficient lens power.
• Corrected with converging lenses to bring the focal point forward.

3. Astigmatism:

• Caused by an irregular cornea curvature, leading to uneven focus.
• Requires cylindrical lenses to focus light evenly on the retina.
• Prescription specifies power and axis angle for correct alignment.