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Minimum deviation

Minimum deviation is a physics 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 Minimum deviation rather than just read about it. In short: In a prism, the angle of deviation (δ) decreases with increase in the angle of incidence (i) up to a particular angle. This angle of incidence, where the angle of deviation in a prism is minimum, is called the minimum deviation position of the prism, and that very deviation angle is known as the minimum angle of deviation (denoted by δmin, Dλ, or Dm).

Minimum deviation — main illustration
Minimum deviation — illustration

Key takeaways

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

Reference excerpt

In a prism, the angle of deviation (δ) decreases with increase in the angle of incidence (i) up to a particular angle. This angle of incidence, where the angle of deviation in a prism is minimum, is called the minimum deviation position of the prism, and that very deviation angle is known as the minimum angle of deviation (denoted by δmin, Dλ, or Dm).

The angle of minimum deviation is related to the refractive index as:

n 21 = sin ⁡ ( A + D m 2 ) sin ⁡ ( A 2 ) {\displaystyle n_{21}={\dfrac {\sin \left({\dfrac {A+D_{m}}{2}}\right)}{\sin \left({\dfrac {A}{2}}\right)}}}

This is useful to calculate the refractive index of a material. Rainbows and haloes occur at minimum deviation. Also, a thin prism is always set at minimum deviation.

Formula

In minimum deviation, the refracted ray in the prism is parallel to its base. In other words, the light ray is symmetrical about the axis of symmetry of the prism. Also, the angles of refractions are equal i.e. r1 = r2. The angle of incidence and angle of emergence equal each other (i = e). This is clearly visible in the graph below. The formula for minimum deviation can be derived by exploiting the geometry in the prism. The approach involves replacing the variables in the Snell's law in terms of the Deviation and Prism Angles by making the use of the above properties.

From the angle sum of △ O P Q {\textstyle \triangle OPQ} ,

A + ∠ O P Q + ∠ O Q P = 180 ∘ {\displaystyle A+\angle OPQ+\angle OQP=180^{\circ }}

⟹ A = 180 ∘ − ( 90 − r ) − ( 90 − r ) {\displaystyle \implies A=180^{\circ }-(90-r)-(90-r)}

⟹ r = A 2 {\displaystyle \implies r={\frac {A}{2}}}

Using the exterior angle theorem in △ P Q R {\textstyle \triangle PQR} ,

D m = ∠ R P Q + ∠ R Q P {\displaystyle D_{m}=\angle RPQ+\angle RQP}

⟹ D m = i − r + i − r {\displaystyle \implies D_{m}=i-r+i-r}

⟹ 2 r + D m = 2 i {\displaystyle \implies 2r+D_{m}=2i}

⟹ A + D m = 2 i {\displaystyle \implies A+D_{m}=2i}

⟹ i = A + D m 2 {\displaystyle \implies i={\frac {A+D_{m}}{2}}}

This can also be derived by putting i = e in the prism formula: i + e = A + δ From Snell's law,

n 21 = sin ⁡ i sin ⁡ r {\displaystyle n_{21}={\dfrac {\sin i}{\sin r}}}

∴ n 21 = sin ⁡ ( A + D m 2 ) sin ⁡ ( A 2 ) {\displaystyle \therefore n_{21}={\dfrac {\sin \left({\dfrac {A+D_{m}}{2}}\right)}{\sin \left({\dfrac {A}{2}}\right)}}}

… excerpt ends here. Continue reading the full article.

Illustrations

Minimum deviation: Light is deflected as it enters a material with refractive index > 1.
Light is deflected as it enters a material with refractive index > 1.
Minimum deviation: A ray of light is deflected twice in a prism. The sum of these deflections is the deviation angle.
A ray of light is deflected twice in a prism. The sum of these deflections is the deviation angle.
Minimum deviation: When the entrance and exit angles are equal, the deviation angle of a ray passing through a prism will be minimal.
When the entrance and exit angles are equal, the deviation angle of a ray passing through a prism will be minimal.
Minimum deviation illustration
Minimum deviation: In this graph of the angle of deviation vs the angle of incidence, δ corresponds to two values of i and e(i'). For minimum deviation, however, i equals e.
In this graph of the angle of deviation vs the angle of incidence, δ corresponds to two values of i and e(i'). For minimum deviation, however, i equals e.

Worked examples

Example 1 — a first encounter with Minimum deviation

Start with the simplest possible case. Write down what Minimum deviation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, 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 Minimum deviation 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 Minimum deviation 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 Minimum deviation

In research
Minimum deviation appears in physics 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 Minimum deviation 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
Minimum deviation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Geometrical optics, Light, so understanding it makes those chapters shorter.
In everyday life
Look for Minimum deviation 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 Minimum deviation in 20 minutes

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

Frequently asked questions

What is Minimum deviation in simple terms?

In a prism, the angle of deviation (δ) decreases with increase in the angle of incidence (i) up to a particular angle. This angle of incidence, where the angle of deviation in a prism is minimum, is called the minimum deviation position of the prism, and that very deviation angle is known as the mi…

Why does Minimum deviation matter?

Because it connects several physics 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 Minimum deviation?

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 Minimum deviation.

Tags

  • Geometrical optics
  • Light

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