Angular Resolution Calculator

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Dominik Czernia, PhD

Dominik Czernia

PhD, Institute of Nuclear Physics PAN

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Dominik Czernia, PhD, is a physicist at the Institute of Nuclear Physics in Kraków, specializing in condensed matter physics with a focus on molecular magnetism. He has led several national research projects, pioneering innovative approaches to novel materials for high technology. Passionate about making science accessible, Dominik has created various calculators, mostly in physics and math categories. In his free time, he enjoys family walks, city explorations, mountain hiking, and traveling everywhere by bike. See full profile

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Bogna Szyk and Adena Benn

Adena Benn

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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This angular resolution calculator will assist you in determining the angular resolution of a lens – the ability of an instrument to distinguish small details of an object. Keep reading if you wish to learn the answers to questions such as:

What does the angular resolution measure?
What is resolution in microscopy?

Read on to find answers to these questions and learn about the angular resolution formula.

What does angular resolution measure?

Angular resolution is the capacity of an optical instrument to separate two objects that are located at a small angular distance. In other words, with this physical quantity, you can check if you can:

Resolve two small points that are very close to each other; or
Distinguish between very distant objects that seem close to each other.

The smaller the angular resolution is, the more details you can see. It is essential when designing microscopes, telescopes, or cameras. Even the human eye has its angular resolution!

If you are interested in learning about telescope magnification, check our telescope magnification calculator.

Angular resolution formula

Angular resolution is sometimes called the Rayleigh criterion. The famous physicist, Lord Rayleigh, has proposed an empirical angular resolution formula:

θ = 1.22 × λ / d

where:

θ – Angular resolution (expressed in radians);
λ – Wavelength of the light; and
d – Diameter of the lens aperture.

The above formula was derived for diffraction grating, but it can also be used for other purposes. Lord Rayleigh stated that two light sources are regarded as resolved when the principal diffraction maximum of one image coincides with the first minimum of the other.

If you are interested in learning more about diffraction grating, see our diffraction grating calculator.

What is the angular resolution of the human eye?

The diameter of an eye pupil (our natural lens) changes during the day and night, but it is approximately 2 mm on sunny days and 8 mm at night. Let's assume that we will try to resolve points that are green; the wavelength of green light is equal to λ ≈ 550 nm. With the Angular resolution calculator, we compute that the angular resolution during the day is θ ≈ 0.02°.

We can compare this result with the Hubble space telescope, which has a mirror of diameter 2.4 m (it collects light just like the eye pupil). The estimated angular resolution equals θ ≈ 0.000016° – it is 125 times better than our eye!

If you enjoyed this calculator, our binoculars range calculator might also interest you.