Optical Density: Formula, Features, Transmittance & Absorbance

Optical density (OD) acts as a useful tool to describe the transmission of light through a highly blocking optical filter at a time when the transmission is extremely small. A higher optical density indicates how much slower the wave travels through that material. When light refracts from one medium to another, one is said to be rarer, while the other is said to be denser. As a result, the term "rarer and denser medium" is a relative one. A rarer medium is one in which the speed of light is greater, whereas a denser medium is one in which the speed of light is lower. In this article, we will discuss optical density, its definition, formula, and some important questions.

Key Terms: Optical Density, Absorption, Refraction, Transmission, Wavelength, Electromagnetic Spectrum, Intensity, Velocity,

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Optical Density

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A material's optical density is the logarithmic ratio of falling radiation to transmitted radiation through it. It can also be defined as a fraction of absorbed radiation at a specific wavelength. The optical density of the medium determines the speed of light, which is determined by the qualities of the medium on which it is incident. The slow tendency of atoms in a material to hold the energy absorbed from an electromagnetic wave in the form of vibrating electrons before being re-emitted as an electromagnetic disturbance is referred to as the optical density of the medium.

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Features of Optical Density

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By contrasting the two mediums, we may better comprehend the phenomenon of optical density and its effect on light flowing through it.

Consider the properties of two different mediums: glass and air. When a light beam travels from the air to the glass, the speed of light slows down. As a result, the light bends towards the normal, as seen in the diagram below:

It indicates that the glass has a higher optical density than air which means:

• The velocity of light in glass (a denser media) is less than in a rarer material (air). 

If the same light flows through the glass and into the air. Light travels at a faster rate. As a result, the light bends away from the normal, therefore: 

• The velocity of light in the air (a rarer media) is less than the velocity of light in glass (denser medium).

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Optical Density Formula

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Optical Density’s formula can be expressed as:

Optical Density (O.D.) = log₁₀ (I_o / I_t)

Where,

• I_o= Intensity of incident light
• I_t= Intensity of transmitted light

The logarithmic ratio of the intensity of incident light (I_o) to the intensity of transmitted light (I_t) flowing through a medium is known as its optical density.

Whereas formula of Absorbance can be expressed as:

A = – log₁₀ (100)/(T%)

Where

T% = 100 (I/I₀)

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Transmittance

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The transmittance of a medium or a material can be defined as the constituent of the light that passes through the other side of the medium. Or in other words, it is the ratio of the light energy falling on it to the light transmitted through it. When light moves through any medium, it can be transmitted, absorbed, or reflected. The transmittance of the light is the ratio of the intensity of incident light (Io) to the amount of intensity (Ia) passing through the medium. It is denoted by T.

Where,

T = l_a/l_o 

Moreover, the transmittance has no unit. 

Therefore, the transmittance (T) is the ratio of radiant flux transmitted by the material (Φ_t) to the radiant flux (Φ_i) twitch is received by that surface. 

Transmittance Formula:

T = Φ_t / Φ_i (the transmittance of the material)

Here, the radiant flux implies the radiant energy emitted, reflected, or received, per unit time. The unit of transmittance is Watt and the SI unit is Joule per second (J/s).

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Absorbance and Optical Density

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Optical density and absorbance are both measurements of light absorption when it travels through an optical material, but they are not the same.

• The ability of an object to slow or delay the transmission of light is measured by optical density.
• It measures the speed of light using a material that is mostly impacted by the wavelength of the light wave in question.
• In a wave motion, absorbance is the transfer of a wave's energy to matter when the wave travels through it.
• The medium is termed to be clear to that particular radiation if there is only a fragmental absorption of energy, but opaque if all of the energy is lost.
• As a result, light is absorbed more readily in an optically thick medium.

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Units of Absorption

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Basically, the absorption unit is used in ultraviolet-visible spectroscopy where AU is a dimensionless quantity. 

Absorption of any material is taken as A,

AU = - log₁₀ (Φ_t / Φ_i) = - log₁₀ T

Where, Φ_t = the radiant flux that is transmitted by that material. 

Φ_i = the radiant flux received by that material. 

T = the transmittance.

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Important Points on Optical Density

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• Higher the optical density, lower is the transmittance.
• The transmission loss is ten times the optical density. 
• This loss is expressed as decibels.

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Things to Remember

• Optical density is defined as the negative of the logarithm of the transmission, where transmission varies between 0 to 1.
• Optical Density’s formula is expressed as: Optical density (O.D.) = log₁₀ (Io / It)
• The formula of Absorbance can be expressed as: A = -log₁₀ (100)/(T%)
• Optical density and absorbance are both measurements of light absorption when it travels through an optical material, but they are not the same.
• The absorption unit is: AU = - log₁₀ (Φ_t / Φ_i) = - log₁₀ T.

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Previous Year Questions

1. Which is true for rays coming from infinity? [DUET 2006]
2. What is the greatest distance of light source visibility? [DUET 2000]
3. What is the hight of the image of the girl visible in the mirror? [KCET 2019]
4. How does the ray suffer when additional equilateral prisms are added? [NEET 2001]
5. Which statement describes the image formed by the object? [NEET 2011]
6. Calculate the focal length of the lens? [NEET 2011]
7. Calculate the focal length and intensity of the lens. [NEET 2010]
8. Calculate the type and power of the correcting lens. [NEET 2016]
9. Calculate the focal length of the combination lens. [NEET 2013]
10. Calculate the angle of incidence. [NEET 2020]
11. Calculate the value of refractive index for the ray to undergo total internal reflection. [NEET 2010]
12. Calculate the length of the image formed by the concave mirror. [NEET 2012]
13. Calculate the refractive angle of the second prism. [NEET 2017]
14. Calculate the angle of the second prism. [NEET 2011]
15. Calculate the thickness of the glass slab. [NEET 2016]
16. What are the specifications of the objective lens of the telescope. [NEET 2018]
17. What should eb the distance betweent he lens to observe the object at 200 cms away. [NEET 2016]
18. Calculate the power of the equiconvex lens. [NEET 2019]
19. Calculate the displacement of the image. [NEET 2018]
20. Calculate the limit of resolution of the telescope with an objective of diameter 2m. [NEET 2020]