Optics

Laurie Sullivan

Refelction and Refraction

Snell’s Law

Snell’s law states that a ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. Mathematically,

ni sin i = nr sinr

Here ni is the index of refraction in the original medium and nr is the index in the medium the light enters. i and r are the angles of incidence and refraction, respectively.

i

r

ni

nr

Willebrord Snell

Snell’s Lawn1/n2=Sin ϴ1/Sin ϴ2

Sin ϴ1

Sin ϴ2

Prisms

Light from air to glass bends towards the normal.

Light from glass to air bends away from the normal.

The image of the object is displaced towards the apex of the prism.

Glass, n2 = 1.5

Air, n1 = 1

30°

øHoriz. ray, parallel to base

Stacked prisms approximate a convex (plus) lens

Converging (plus) lenses

Converging (plus) lenses

Converging (plus) lenses

Converging (plus) lenses

Diverging (minus) lenses

Spherical Aberration

Coma

Chromatic Abberation

Blue bends more than red

Chromatic AberrationAs in a raindrop or a prism, different wave-lengths of light are refracted at different angles (higher frequency ↔ greater bending). The light passing through a lens is slightly dispersed, so objects viewed through lenses will be ringed with color. This is known as chromatic aberration and it will always be present when a single lens is used. Chromatic aberration can be greatly reduced when a convex lens is combined with a concave lens with a different index of refraction. The dispersion caused by the convex lens will be almost canceled by the dispersion caused by the concave lens. Lenses such as this are called achromatic lenses and are used in all precision optical instruments.

Chromatic Aberration

Achromatic Lens

Examples

way out of the droplet, the light is once more refracted and dispersed. Although each droplet produces a complete spectrum, an observer will only see a certain wavelength of light from each droplet. (The wavelength depends on the relative positions of the sun, droplet, and observer.) Because there are millions of droplets in the sky, a complete spectrum is seen. The droplets reflecting red light make an angle of 42o with respect to the direction of the sun’s rays; the droplets reflecting violet light make an angle of 40o. Rainbow images

Rainbows A rainbow is a spectrum formed when sunlight is dispersed by water droplets in the atmosphere. Sunlight incident on a water droplet is refracted. Because of dispersion, each color is refracted at a slightly different angle. At the back surface of the droplet, the light undergoes total internal reflection. On the

The reduced Human eye (Donders)

Vergence

Vergence

• Vergence of a beam. The vergence is inversely proportional to the distance from the focus in metres.

• If a (positive) lens is focussing the beam, it has to sit left of the focus, while a negative lens has to sit right of the focus to produce the appropriate vergence.

Contact lenses (CLs)

1. Soft, hydrophilic hydrogel are better tolerated physically but, less permeable to oxygen.

2. Silicone hydrogel (SiHy) soft lenses have better O2 transmission3. Rigid gas permeable (RGP) have better O2 transmission again Advantages of rigid gas-permeable:

o Their greater oxygen-permeability reduces the risk of corneal damage from hypoxia

o Their rigidity allows easier cleaning and offers less risk of infection

o Their rigidity permits an effective correction of astigmatism and irregular shape

o Proteinaceous debris is less likely to adhere to the lens and cause an allergic conjunctivitis

Contact Lenses (CLs)

• Hard (RGP) contact lenses are mainly used in the treatment of keratoconus or scarred corneas.

• Soft contact lenses for:1) Optical correction (built on to front surface

of the CL)2) Bandage contact lenses for the relief of pain

as with epithelial defects or bullous keratopathy (always use prophylactic topical antibiotics).

Complications Of Contact Lenses

• Superficial punctate keratitis is the most common complication. It is staining at 3 and 9 o’clock and this is associated with incomplete blinking and drying in rigid lens syndrome.

• The tight lens syndrome, characterized by indentation and staining in the conjunctival epithelium in a ring around the cornea.

• Acute hypoxia Epithelial micro cysts, necrosis and endothelial blebs. Corneal oedema, epithelopathy

• Chronic Hypoxia Vascularization and lipid deposition.• Microbial keratitis

Lens Effectivity

Lens effectivity is due to the change in vergence of light that occurs at different points along its path. This is related to vertex distance.

• Formula: Fnew = Fcurrent/(1-dFcurrent) where F is in Diopters and d is in meters.

• When providing a “distance correction”, the principle focal point F2 of the correcting lens must coincide with the far point of the eye. The lens power depends on its location in front of the eye. The closer to the eye the lens is mounted, the shorter is its focal length in the case of hyperopia, and the longer its focal length in the case of myopia. Because of this, plus power has to be added in both cases. Therefore, myopes need less minus and hyperopes need more plus when going from spectacles to contact lenses.