Optics: Lenses, Mirrors, and Eye Vision

Optics: Lenses, Mirrors, and the Eye

An optical lens is a system comprising two or more refractive surfaces, of which at least one is curved.

Types of Lenses

• Convex or Converging Lenses: Thicker in the center, causing rays to converge.
• Concave or Diverging Lenses: Thinner in the central part, causing rays to diverge.

Specific Lens Shapes

• Convex Lenses: Convex, plano-convex, meniscus-convex
• Concave Lenses: Concave, plano-concave, concave meniscus

Image Formation by Convex Lenses

• If s0 > 2f: Real, inverted, smaller image.
• If s0 = 2f: Real, inverted, same size image.
• If 2f > s0 > f: Real, inverted, larger image.
• If s0 = f: No sharp image formed (image at infinity).
• If s0 < f: Virtual, upright, magnified image (magnifying glass).

Image Formation by Concave Lenses

• Always Virtual, upright, smaller image.

Mirrors

Image Formation by Plane Mirrors

• Always Virtual, upright, same size image.

Image Formation by Spherical Concave Mirrors

• If s0 > r: Real, inverted, smaller image.
• If s0 = r: Real, inverted, same size image.
• If r > s0 > f: Real, inverted, larger image.
• If s0 = f: No sharp image formed (image at infinity).
• If s0 < f: Virtual, upright, magnified image.

Image Formation by Spherical Convex Mirrors

• Always Virtual, upright, smaller image.

Eye Anatomy and Optics

Paraxial Rays

Rays that are closest to the optical axis.

The Cornea

The transparent front part of the eye, continuous with the sclera. It acts like a convex lens, refracting rays towards the optical axis. It is slightly flattened to reduce aberrations.

The Iris

Responsible for regulating the amount of light entering the eye. It is constituted by radial and circular muscles, and its color is characteristic of the eyes.

The Lens

A lens with many transparent layers. Its refractive index is not homogeneous. Its elasticity provides the ability to vary its shape (accommodation), allowing for clear vision and proper focus.

The Retina

The optical receiver of the eye. This is a very thin layer constituted by millions of receptor cells called rods and cones.

• Rods are not sensitive to color, which is why we cannot distinguish colors in a dark room.
• There are also no receptor cells at the connection point of the optic nerve, which is why it is called the blind spot.

Common Vision Defects

Astigmatism

A common defect usually due to an irregularly shaped cornea, which may have different curvatures in different planes. This leads to vision that cannot be corrected with clear lenses either.

Presbyopia (Eyestrain)

Due to the loss of flexibility of the lens, reducing the capacity for accommodation. We lose the ability to see nearby objects clearly and tend to stretch our arm to read more comfortably.

Cataracts

The loss of transparency of the lens, which severely hinders vision. It usually occurs in the elderly. Its correction is surgical: the defective lens is removed and replaced with a new artificial one.