science

Troland

Troland is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Troland rather than just read about it. In short: The troland (symbol Td), named after Leonard T. Troland, is a unit of conventional retinal illuminance.

Key takeaways

Troland belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Troland to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Troland from memory before moving on to harder problems.

Reference excerpt

The troland (symbol Td), named after Leonard T. Troland, is a unit of conventional retinal illuminance. It is meant as a method for correcting photometric measurements of luminance values impinging on the human eye by scaling them by the effective pupil size. It is equal to retinal illuminance produced by a surface whose luminance is one nit when the apparent area of the entrance pupil of the eye is 1 square millimeter. The troland unit was proposed in 1916 by Leonard T. Troland, who called it a photon. The troland typically refers to the ordinary or photopic troland, which is defined in terms of the photopic luminance:

T = L × p , {\displaystyle T=L\times p,}

where L is the photopic luminance in cd⋅m−2 and p is pupil area in mm2. A scotopic troland is also sometimes defined:

T ′ = L ′ × p , {\displaystyle T'=L'\times p,}

where L′ is the scotopic luminance in cd⋅m−2 and p is pupil area in mm2. Although named "retinal illuminance" (and originally named "photon" by Troland), trolands do not measure the actual photon flux incident on the retina; that quantity depends on the specific wavelengths of light that constitute the luminance used in the calculation.

Units conversion Troland does not directly convert to other units, being a retinal luminance per unit area of a pupil. However Troland is linked to retinal illuminance in lux = lm/m2 as follows. Assuming the corneal luminance L from an extended source, the pupil diameter p and the focal length of the eye F, the retinal luminance is:

Lr [lm/m2] = π ⋅ L / 4 / (f/#)2 ≈ π ⋅ L ⋅ p2 / 4 / F2. Multiplying by the pupil area: Trolands [cd/m2 ⋅ mm2] = L ⋅ π ⋅ p2/4 = F2 ⋅ Lr ≈ 289 ⋅ Lr. Alternatively, the retinal illuminance Lr [lm/m2] = Trolands / 289 [mm2]. As provided by a more accurate optical calculations, the conversion factor is 278 rather than 289 as demonstrated by simplified considerations above. Sometimes (by convention only, although not rigorously accurate by definition), retinal luminance is expressed in [cd/m2] = [lm/sr/m2]. Assuming a Lambertian surface, 1 cd/m2 = π lm/m2 = π lux. That is, 1 [cd/m2] = 289/π [Troland] ≈ 92 [Troland]

Physical quantities luminance equivalent luminance

Unit system centimeter–gram–second (CGS)

Basic unit dimensions [length]−2 [luminous intensity]

Comparisons ≈ 0.8 × luminance of a kerosene candle (≈ 12000 cd/m2 ) ≈ luminance of a sperm candle (≈ 10000 cd/m2 ) ≈ luminance of an average daytime clear sky (≈ 8000 cd/m2)

See also Leonard T. Troland Troland Research Awards

References

Worked examples

Example 1 — a first encounter with Troland

Start with the simplest possible case. Write down what Troland claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Troland before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Troland ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Troland

In research: Troland appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Troland in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Troland is common in secondary-school and first-year university syllabi. It links to neighbouring topics Non-SI metric units, Units of illuminance, Vision, so understanding it makes those chapters shorter.
In everyday life: Look for Troland outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Troland in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Troland means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Troland out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Troland in simple terms?

The troland (symbol Td), named after Leonard T. Troland, is a unit of conventional retinal illuminance.

Why does Troland matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Troland?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Troland.