# Optical Parameters

### 1. Wavelength λ

The propagation of light can be described using the electromagnetic wave theory. The distance separating one crest of a light wave from the next is the wavelength λ.
The range of optical radiation (100 nm - 1 mm) covers the regions ultraviolet (UV), visible light (VIS) and infrared (IR). The wavelengths of visible light lie between 380 and 780 nm. To describe a certain colour of visible light, the wavelength is specified in air.

Refraction of light at the air / lens interface

### 2. Refractive index n

The refractive index n of a lens specifies the ratio of the velocity of light in air to the velocity of light in the lens.

Due to a reduction in its velocity in the lens, the light undergoes a change of direction if it is obliquely incident on the lens surface. This process is known as refraction. The higher the refractive index of the material, the greater the reduction in the light’s velocity and the greater its refraction. Light is more strongly refracted by lenses with a high refractive index.

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Reflection, absorption and transmission

### 3. Reflection, Absorption and Transmission

When the light incident on the lens actually passes through the lens, it is attenuated by reflection at the interfaces and by absorption in the lens material.

Reflectance with perpendicular incidence of light

#### Reflectance ρ

Reflectance is the ratio of reflected light to incident light at an interface between two optical media. If the reflectance is multiplied by 100, the percentage of reflected light is obtained. Providing lenses with an antireflection coating reduces the amount of reflected light and hence increases the transmission of the lens.

#### Absorptance α and Transmittance τ

Absorptance α

The attenuation of light when it passes through a lens is known as absorptance. The darker a lens, the higher absorptance becomes.

Transmittance τ

Transmission means the ability of a lens to let light through. The transmittance of a lens is the ratio of emergent light to incident light. Transmittance in a lens with an antireflection coating is higher than in an identical, uncoated lens.

#### Light reduction factor

The sum of reflectance and absorptance provides the light reduction factor. The light reduction factor is an important parameter in ophthalmic optics and is specified as a percentage to indicate the degree of tinting to which a lens has been subjected.

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Dispersion

### 4. Dispersion

Every colour of light, characterised by its wavelength in air, propagates at a different velocity in the lens. The shorter the wavelength, the lower the velocity of light in the lens. It is for this reason that short-wave blue light is more strongly refracted than long-wave red light. Different refractive indices can therefore be given for red, green and blue light.

If white light is refracted at a lens, it is split up into its various colour components, as each colour is refracted differently. This phenomenon is known as dispersion.

The mean dispersion Δn gives the difference between nF’ and nC’ .

When specifying the refractive indices of optical media, the mean refractive index ne is always used.

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Refractive index and Abbe number

### 5. Abbe number ν

The Abbe number is used to describe the dispersion properties of a lens. It is the ratio of the angle of deflection δe to the mean dispersion angle δF’C’ .
A low Abbe number indicates a high level of dispersion. The Abbe number should not be lower than 30 to ensure that colour fringes do not impair peripheral vision.

The higher the refractive index n:

• the higher the reflectance ρ
• the higher the mean dispersion Δn
• the lower the Abbe number ν
• the lower the transmittance τ
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### 6. Equivalent Power F

The equivalent power F is the reciprocal of the focal length measured in metres. Like the equivalent power of an optically effective surface, the equivalent power of a spectacle lens is given in dioptres (D).

The surface power is determined by the ratio of the difference between the refractive indices of two media to the radius of curvature of this surface. The two surface powers F1 and F2 yield the equivalent power F of a lens, taking into account the centre thickness t.

Parameters for determining the equivalent power

### 7. Back vertex power F’n

In ophthalmic optics not only the equivalent power Fn but also the back vertex power F’n is used to denote the power of a lens. It is the reciprocal of the back vertex focal length f’n given in metres.

A focimeter is used to measure the back vertex power of a lens.

### 8. Shape factor S

The image on the retina of an eye corrected with spectacles is different in size to the retinal image of an emmetropic (normal) eye of the same length. This difference in image size is dependent on the shape factor of the lens as well as on other factors.

The shape factor is the ratio of the back vertex power to the equivalent power. In a lens of finite thickness the equivalent power and the back vertex power differ (F≠F’n). The shape magnification S is then greater than 1 (S > 1). An imaginary infinitely thin lens has a shape factor of 1 (S = 1), i. e. F’n = F is only the case for an infinitely thin lens.

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