Come on, people! The "allowed range" depends on the linear range of the used spectrometer! With a cheap one, you might not even be able to measure OD=2, while a PerkinElmer Lambda 900 or Varian Cary 5000 is even able to accurately measure OD=6 (if used properly). A general rule is nonsense!

There are problems with the optical density between 3 and 4. D must be lower then 2. To back calculate the absorbance from optical density, please read:

C. A. Parker Photoluminescence of solutions” (1968).

I absolutely agree with Vladimir "D must be lower then 2"

" please suggest me to back calculate the absorbance from optical density."

IUPAC recommendation:

optical density [obsolete]

Synonymous with absorbance. The use of the term optical density is discouraged.

Source:

PAC, 1996, 68, 2223 (Glossary of terms used in photochemistry (IUPAC

Recommendations 1996)) on page 2257

absorbance, Math - title

Logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls). Depending on the base of the logarithm a decadic and Napierian absorbance are used. Symbols: Math - text, Math - text, Math - text. This quantity is sometimes called extinction, although the term extinction, better called attenuance, is reserved for the quantity which takes into account the effects of luminescence and scattering as well.

Source:

Green Book, p. 32

See also:

PAC, 1996, 68, 2223 (Glossary of terms used in photochemistry (IUPAC Recommendations 1996)) on page 2226

PAC, 1990, 62, 2167 (Glossary of atmospheric chemistry terms (Recommendations 1990)) on page 2169

Value between 3 and 4 is erroneous and it is better to dilute your solution and read the absorbance for more accuracy value.

Agree with all. Less than 2.

Direct measurement of absorbance value between 3 and 4 is not acceptable. But if the value has been obtained by diluting the sample, measuring the absorbance of the solution and then multiplying the measured absorbance with dilution factor then the values are trustable and can be used in a standard curve for concentration determination.

The term "Optical Density" should be fine when one is measuring microbial cell density.

Dear V. N.Ravi Kishore V.

Why the term "absorbance" is preferable when one is measuring microbial cell density?

Again " optical density [obsolete]

Synonymous with absorbance. The use of the term optical density is discouraged. " 

I think both terms "Absorbance" and "Optical Density" should be distinguished.

For absorbing molecules, when the attenuation in light intensity is due to a chromophore absorbing a photon, the term "absorbance" is correct term. But when you are measuring microbial cell cultures, there is no absorbing chromophore there, the attenuation in light intensity is due to scattering. Photons don't reach the detector due to scattering by microbial cells. I think this should be distinguished from intensity attenuation due to chromophore absorption.

Absorbance - when attenuation of light intensity is due to photon absorption by the chromophore

Optical density - when attenuation in light intensity occurs due to photons getting scattered in other directions and hence don't reach the detector.

In both the measurements the way the experiment is performed, the formula used, all being the same.

Dear V. N.Ravi Kishore V., 

In order to avoid any confusions in discussions and publications we MUST use the generally accepted definitions. In chemistry the recommended  definitions are collected in the "IUPAC Gold Book."  Your definitions are not consistent with the recommended by IUPAC. 

I am suggesting that both the scenarios mentioned above should be distinguished. Is it fair/correct to denote both the scenarios with a single parameter?

Neither me nor you establish the rules. You can write your suggestions to IUPAC. I often disagree with IUPAC definitions, but I must follow them. 

I am surprised that IUPAC did not consider these views.

Thank you all for your valuable suggestions.

Just for completeness: IUPAC actually considers systems where you have both, absorption and scattering. In this case the correct term is attenuance, see

https://goldbook.iupac.org/A00513.html

Is it not good to have different terms for different things? Just to avoid confusion.

Same term can lead to confusion. Just imagine two people talking to each other. Both of them use the same term but they are intending different things.

That's why you must follow IUPAC recommendations

Come on, people! The "allowed range" depends on the linear range of the used spectrometer! With a cheap one, you might not even be able to measure OD=2, while a PerkinElmer Lambda 900 or Varian Cary 5000 is even able to accurately measure OD=6 (if used properly). A general rule is nonsense!

With ten fold dilution of absorbance = 4 sample, you will not  be in the linear range.