Understanding Optics: The Magnifying Glass and the Human Eye

The Magnifying Glass

A magnifying glass consists of a converging lens that allows us to see objects appear larger than they are. To observe a small object in detail, we bring it closer to the eye to create a larger image on the retina. However, bringing an object too close limits our ability to see it clearly. A magnifying glass allows us to place the object closer than the eye's normal near point.

The angular magnification, or magnifying power, of a magnifier is the ratio between the visual angle (γ) of the object observed with the lens and the visual angle (γ₀) of the object seen without the lens when placed at the near point.

Formulas for Angular Magnification

γ ≈ tan(γ) = y / f
γ₀ ≈ y / 0.25
Aₐ = γ / γ₀ = 0.25 / f

The Human Eye

The purpose of the human eye is to provide stigmatic and flawless images of objects. Its shape is roughly spherical, providing a wide field of view of about 180°. It can rapidly adjust its focus, a process called accommodation, for the vision of both near and distant objects. The perceived size of an object is determined by the size of the image formed on the retina. The near point of a normal human eye is about 25 cm.

Parts of the Eye

• Retina
• Sclera
• Choroid
• Lens
• Cornea
• Pupil
• Aqueous Humor
• Iris
• Vitreous Humor

Common Eye Defects

Myopia (Nearsightedness)

Myopia is a condition where a person can focus on nearby objects but not on distant ones. The far point is at a finite distance, which may be only a few meters. This defect occurs when images are formed in front of the retina instead of on it. It can be corrected using diverging lenses, which refract light rays away from the principal axis, allowing the eye's lens to focus the image correctly on the retina.

Hyperopia (Farsightedness)

Hyperopia is the difficulty in focusing clearly on close objects. The near point of the eye is farther away than normal. This defect is due to the eye's lens not being sufficiently convergent or the eyeball being too short. As a result, the image is formed behind the retina, causing blurry vision. Converging lenses can correct this defect by refracting light rays toward the principal axis, which allows the eye's lens to converge them properly so the image forms on the retina.