Diopter and Dioptric Power | It’s relation with Magnifying Power

Dioptric Power

What does Diopter refer to?

The unit of measurement of Optical Power of a curved mirror or a lens is referred to as Diopter (D). Dioptric power is given by the reciprocal of the focal length of the lens surface or mirror (in meters), i.e. [1D = 1 m-1]. For example, a lens with a focal length of ½ meters has an optical power of 2D. A plane mirror or a flat glass has a focal length equal to infinity (∞) and optical dioptric power equal to zero; therefore, they cannot converge or diverge light rays.

What does the term Dioptrics refer to?

The term Dioptrics refers to the study of refraction of light through lenses. Telescopes that use a convex lens are often called ‘dioptric‘ telescopes. Alhazen, the father of modern optics, conducted initial studies of dioptrics.

Who found the relation between optical power and focal length?

In 1866, Albrecht Nagel was the first person to suggest optical power (the reciprocal of focal length) for labeling/numbering lenses. Later in 1872, a French ophthalmologist Ferdinand Monoyer coined the term diopter for optical/refracting power influenced by Johannes Kepler’s term dioptrice.  The international system of the unit has not included any official symbol for Diopter. However, the symbols D or dpt. are commonly used. 

Why is using dioptric power preferred over focal length in the lensmaker’s equation?

The lensmaker’s equation

uses the reciprocal of focal length. Therefore, by using optical power, the calculations become simple, and simply adding the powers can give the approximate focal length when the thickness of the lens is negligible. For example, if a thin 1-dioptre lens is placed very close to a thin 2-dioptre lens, then the power of the resulting lens system is approximately 3-dioptre. 

What is the optical dioptric power for a human eye?

 An average human relaxed eye has the optical power of approximately 60 diopters. The crystalline eye lens accounts for just 1/3 of the total refractive power (i.e., around 20 diopters). The cornea contributes the remaining 2/3rd of the refractive power (i.e., around 40 diopters).  

An interesting fact about the human eye is that it can vary/adjust its optical power to a certain extent. This ability of a human eye to alter its optical power is termed as the amplitude of accommodation. This is achieved by the contraction and relaxation of the ciliary muscles according to the eye’s tension/stress, the object to be focused, and the amount of light received. This ability, however, weakens with age. Till the age of 15, the human eye can accommodate 11 to 16 diopters that decrease to 10 diopters at 25. This further decreases to 1 diopter after reaching the age of 60. 

What is the nature of the dioptric power of spherical lenses and mirrors?

Concave lenses are associated with negative optical dioptric power i.e., these lenses have a diverging power.

Convex lens Image source: User Fir0002 on en.wikipedia

Convex lenses are associated with positive optical dioptric power i.e., these lenses have a converging power.

dioptric power
Convex lens Image source: User Fir0002 CC BY-SA 3.0

The power of these lenses is measured by using a lensometer, and the power of the eye is measured by autorefractor. 

Convex mirrors are associated with negative optical power i.e., these mirrors have a diverging power and are commonly used as rearview mirrors in vehicles.

Convex mirror
Image source: Ildar Sagdejev (Specious), 2008-03-14 Convex mirror in Atlanta garage entranceCC BY-SA 4.0

Concave mirrors are associated with positive optical power i.e., these mirrors have a converging power and are commonly used in shaving mirrors and telescopes. 

Concave mirror Image source: AfroBrazilianDental Mirror 01CC BY-SA 3.0

What is the relation between Magnifying Power and Optical Dioptric Power?

A simple magnifying glass with a magnifying power V is related to the optical power φ of the glass by 

V = 0.25m x φ + 1

This expression gives the approximate magnification observed by a person with normal vision when using a magnifying glass to view an object.

This shows that magnifying power is directly proportional to optical power. Hence, with an increase in magnifying power, dioptric power also increases. 

What is the relation between Optical Dioptric Power and Curvature?

The curvature of a lens can be measured in dioptres as the reciprocal of the radius of the lens (in meters). For example, if a spherical lens has a radius of 1/5 meter, then its curvature is 5 dioptres. 

Let C be the curvature of one of the surfaces a lens and n be the refractive index of the lens. Then, the optical power of the lens is given by 

φ = (n − 1)C 

This shows that optical power is directly proportional to the curvature of a lens. The more the curvature, the more is the power.  When a lens has curved surfaces on both sides, then their curvatures can be considered positive for the lens and added. This can be followed only when the lens thickness is much smaller than the radius of curvatures.  In the case of a mirror, the optical power is given by φ = 2C (where C is the curvature of the reflecting side.)

To know more about lensometer visit https://lambdageeks.com/a-detailed-overview-on-lensometer-working-uses-parts/ & for autorefractor visit https://lambdageeks.com/autorefractor/

About Sanchari Chakraborty

I am an eager learner, currently invested in the field of Applied Optics and Photonics. I am also an active member of SPIE (International society for optics and photonics) and OSI(Optical Society of India). My articles are aimed towards bringing quality science research topics to light in a simple yet informative way. Science has been evolving since time immemorial. So, I try my bit to tap into the evolution and present it to the readers.

Let's connect through https://www.linkedin.com/in/sanchari-chakraborty-7b33b416a/