Formula
Refraction through prism
δ = (i₁ + i₂) - A, where A is prism angle. At minimum deviation (i₁ = i₂): n = sin((A+δ_m)/2) / sin(A/2).
-- NCERT Class 12 Physics, Ch. 9, p. 240Refraction Prism
8 MCQs1 revision card9-step worked example
Source: NCERT OpticsPYQ coverage: NEET 2021Official key: NTA-verifiedLast updated: 26 Sep 2026
Refraction Prism, explained for NEET
The prism trap is a bookkeeping trap, not a physics trap. A prism problem hands you four angles that look interchangeable — i₁, r₁, r₂, i₂ — plus the prism angle A and the deviation δ. Students who know every relation still lose the mark by dropping δ = i₁ + i₂ − A, or by feeding a non-symmetric ray path into the minimum-deviation formula, or by leaving the calculator in radian mode through an inverse sine. The documented trap for this topic is exactly this: cumulative trig and inverse-trig error across a three-step path.
Fix it with fixed bookkeeping. At the first face, sin i₁ = n sin r₁. Inside the prism, the geometry of the triangle forces r₁ + r₂ = A — always, for any ray. At the second face, n sin r₂ = sin i₂. The total deviation is δ = i₁ + i₂ − A.
Deviation is not monotonic in i₁. Plot δ against i₁ and you get a curve with a single minimum, reached when the path is symmetric: i₁ = i₂, and therefore r₁ = r₂ = A/2. Only at that point may you write
n = sin[(A + δₘ)/2] / sin(A/2)
NCERT Class 12 Physics Part 2, Chapter 9, page 240 states this formula with the minimum-deviation condition attached. The condition is part of the formula. Apply it to a general incidence angle and the number you get is not the refractive index of anything.
For a thin prism — A small enough that sines may be replaced by angles — the relation collapses to δ = (n − 1)A, independent of i₁. This is the small-angle result NEET asks for when it gives you A and n and no incidence angle at all. Spotting which of the two forms a question wants is the single decision that determines whether the problem takes 20 seconds or 90.
Watch-out: if a question says "angle of minimum deviation" it is handing you symmetry. If it merely says "deviation," you must build δ from i₁ + i₂ − A yourself.
Can you answer these Refraction Prism MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
For a ray passing through a prism of refracting angle A, the two angles of refraction inside the prism, r₁ at the first face and r₂ at the second face, always satisfy
Show answer and why every option is right or wrong
Answer: D. D is correct. The normals at the two refracting faces meet at an angle 180° − A, and the triangle formed inside the prism forces r₁ + r₂ = A for every ray, symmetric or not. This geometric relation is stated alongside the prism formula in NCERT Class 12 Physics Part 2, Chapter 9, page 239.
Why A is wrong: A is wrong because it confuses the angle between the refracted rays and the faces with the angle between them and the normals.
Why B is wrong: B is wrong because r₁ − r₂ = A holds for no ray; at symmetric incidence r₁ = r₂ = A/2, so the difference is zero while A is not.
Why C is wrong: C is wrong because it would give r₁ = r₂ = A at minimum deviation, twice the correct A/2, and would exceed the critical angle for most prisms.
MCQ 2Easy RecallPractice
The prism formula n = sin[(A + δₘ)/2] / sin(A/2) may be applied only when
Show answer and why every option is right or wrong
Answer: C. C is correct. The formula is derived at minimum deviation, where the ray path is symmetric — i₁ = i₂, and consequently r₁ = r₂ = A/2. NCERT Class 12 Physics Part 2, Chapter 9, page 240 attaches this condition to the formula itself.
Why A is wrong: A is wrong because the formula holds for any refractive index; n is the quantity it returns, not a restriction on its use.
Why B is wrong: B is wrong because normal incidence gives r₁ = 0, so r₂ = A — an asymmetric path, which is the one case the formula certainly does not cover.
Why D is wrong: D is wrong because it confuses this exact formula with the thin-prism approximation δ = (n − 1)A, which is the one that requires small A.
MCQ 3Easy RecallPractice
As the angle of incidence on the first face of a prism is increased steadily from a small value, the angle of deviation δ
Show answer and why every option is right or wrong
Answer: B. B is correct. The δ-versus-i₁ curve has a single minimum, occurring at symmetric incidence. This behaviour is the reason a minimum deviation exists at all and is described with the prism formula in NCERT Class 12 Physics Part 2, Chapter 9, page 240.
Why A is wrong: A is wrong because a monotonically increasing δ would have no minimum, and the quantity δₘ in the prism formula would not exist.
Why C is wrong: C is wrong for the same reason as A, with the direction reversed; δ also rises again at grazing incidence.
Why D is wrong: D is wrong because δ depends on A and n only in the thin-prism limit; for a finite prism δ varies with the angle of incidence.
MCQ 4Direct ApplicationPractice
A prism has a refracting angle of 60.0°. A ray passes through it symmetrically with an angle of minimum deviation of 30.0°. The angle of refraction at the first face is
Show answer and why every option is right or wrong
Answer: A. A is correct. At minimum deviation the path is symmetric, so r₁ = r₂ = A/2 = 60.0°/2 = 30.0°. The symmetry condition r₁ = r₂ = A/2 accompanies the prism formula in NCERT Class 12 Physics Part 2, Chapter 9, page 240; δₘ is not needed for this step.
Why B is wrong: B is wrong because it computes (A + δₘ)/2 = 45.0°, which is the argument of the numerator sine in the prism formula, not the internal refraction angle.
Why C is wrong: C is wrong because it halves A twice, or reads δₘ/2 as though δₘ were the internal angle.
Why D is wrong: D is wrong because it takes r₁ = A, which would require r₂ = 0 and hence normal emergence — an asymmetric path incompatible with minimum deviation.
MCQ 5Direct ApplicationPractice
A thin prism of refracting angle 4.00° is made of material of refractive index 1.50. The deviation produced by the prism is
Show answer and why every option is right or wrong
Answer: D. D is correct. For a thin prism the deviation is δ = (n − 1)A = (1.50 − 1) × 4.00° = 2.00°, and it does not depend on the angle of incidence. This small-angle form follows from the prism formula of NCERT Class 12 Physics Part 2, Chapter 9, page 240 when both sines are replaced by their arguments.
Why A is wrong: A is wrong because it uses δ = nA instead of (n − 1)A, keeping the whole refractive index rather than the excess over unity.
Why B is wrong: B is wrong because it computes A/n = 4.00°/1.50 = 2.67°, dividing by n where the thin-prism formula multiplies by (n − 1).
Why C is wrong: C is wrong because it reports A itself as the deviation, which would mean the deviation is independent of the material.
MCQ 6Direct ApplicationPractice
A ray enters a prism of refracting angle 50.0° with an angle of incidence of 40.0° and emerges with an angle of emergence of 62.0°. The angle of deviation is
Show answer and why every option is right or wrong
Answer: A. A is correct. Deviation is built from the two external angles and the prism angle: δ = i₁ + i₂ − A = 40.0° + 62.0° − 50.0° = 52.0°. The relation is part of the standard prism bookkeeping given with the formula in NCERT Class 12 Physics Part 2, Chapter 9, page 239.
Why B is wrong: B is wrong because it computes i₂ − i₁ = 22.0°, the difference between the external angles, which is not the deviation.
Why C is wrong: C is wrong because 102.0° is i₁ + i₂ = 40.0° + 62.0° with the prism angle left out. The deviation is i₁ + i₂ − A = 102.0° − 50.0° = 52.0°.
Why D is wrong: D is wrong because it computes i₂ − A = 12.0°, discarding the incidence angle entirely.
MCQ 7CalculationPractice
A prism of refracting angle 60.0° is made of a material for which the angle of minimum deviation is also 60.0°. The refractive index of the material is (take sin 60.0° = 0.866, sin 30.0° = 0.500)
Show answer and why every option is right or wrong
Answer: B. B is correct. Applying n = sin[(A + δₘ)/2] / sin(A/2) = sin[(60.0° + 60.0°)/2] / sin(30.0°) = sin 60.0° / sin 30.0° = 0.866 / 0.500 = 1.73. The formula and its minimum-deviation condition are given in NCERT Class 12 Physics Part 2, Chapter 9, page 240.
Why A is wrong: A is wrong because it takes the ratio of the angles, (A + δₘ)/2 ÷ A/2 = 60.0/30.0, instead of the ratio of their sines — the most common way the trig step is skipped.
Why C is wrong: C is wrong because it evaluates sin[(A + δₘ)/2] / sin(A/2) with both arguments taken as A/2, giving unity and implying no refraction at all.
Why D is wrong: D is wrong because 1.15 = 1/sin 60.0° applies the critical-angle relation n = 1/sin C, with 60.0° taken as the critical angle; that relation has nothing to do with minimum deviation.
MCQ 8Concept TrapPractice
A student measures a prism's deviation at one arbitrary angle of incidence, obtains δ = 44.0° for a prism of refracting angle 60.0°, and substitutes this δ into n = sin[(A + δ)/2] / sin(A/2). The value obtained is
Show answer and why every option is right or wrong
Answer: C. C is correct. δₘ is the minimum of the deviation curve, so any deviation measured at non-symmetric incidence is larger than δₘ; substituting it into a formula derived under the symmetry condition returns a number that is not the material's refractive index. The condition is stated with the formula in NCERT Class 12 Physics Part 2, Chapter 9, page 240.
Why A is wrong: A is wrong because it drops the minimum-deviation condition from the formula — the documented cumulative-error trap for prism problems.
Why B is wrong: B is wrong because no factor of 2 relates the two; the error is one of validity, not of scaling.
Why D is wrong: D is wrong because it inverts the direction of the inequality: δₘ is the smallest possible deviation, so a general δ is larger, not smaller.
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Refraction Prism: quick recall before you leave
How do you solve a Refraction Prism question? A worked example
- 1
Given
• Refracting angle of prism, A = 60.0°• Refractive index of prism material, n = 1.50• The ray passes through at minimum deviation.• Trigonometric data supplied: sin 30.0° = 0.500; sin 48.6° = 0.750.
- 2
Required
The angle of minimum deviation δₘ, and the angle of incidence at which it occurs.
- 3
Concept
At minimum deviation the ray path through the prism is symmetric about the bisector of the refracting angle. That symmetry fixes r₁ = r₂ = A/2, which is what makes a single closed-form relation between n, A and δₘ possible. Away from that point the deviation depends on the angle of incidence and no such closed form exists.
- 4
Formula
n = sin[(A + δₘ)/2] / sin(A/2), together with δ = i₁ + i₂ − A and i₁ = i₂ at minimum deviation.
- 5
Substitution
1.50 = sin[(60.0° + δₘ)/2] / sin(30.0°)
- 6
Calculation
sin[(60.0° + δₘ)/2] = 1.50 × sin 30.0° = 1.50 × 0.500 = 0.750
The constants here are exact in the sig-fig sense: the 2 in A/2 and in (A + δₘ)/2 is a counting divisor from the symmetry condition, not a measurement, so it does not limit the precision of the result. The three significant figures come from A and n.
(60.0° + δₘ)/2 = arcsin(0.750) = 48.6°
60.0° + δₘ = 97.2°
δₘ = 37.2°
For the incidence angle: with i₁ = i₂ and δₘ = i₁ + i₂ − A, we get 37.2° = 2i₁ − 60.0°, so i₁ = 48.6°. - 7
Final answer
δₘ = 37.2°, occurring at an angle of incidence i₁ = 48.6°.
(Note the coincidence worth recognising: i₁ = (A + δₘ)/2 always, since i₁ = i₂ at minimum deviation. That is why 48.6° appears twice.) - 8
Common trap
The documented prism trap is cumulative trig error across the three steps. Three failure points in this one problem: multiplying 1.50 by 30.0 instead of by sin 30.0° (giving 45, a meaningless "sine"); reading 48.6° as δₘ rather than as (A + δₘ)/2 and stopping one step early; and leaving the calculator in radian mode for the arcsin, which returns 0.848 and then gets reported as degrees. Each is a single keystroke and each costs the full negative mark. Guard by checking the sine argument is between −1 and 1 before taking the inverse, and by confirming your δₘ satisfies δₘ = 2i₁ − A afterwards.
- 9
Similar NEET-style question
A prism of refracting angle 60.0° is immersed in a liquid, and the angle of minimum deviation is found to drop to 10.0°. Given sin 35.0° = 0.574 and sin 30.0° = 0.500, find the refractive index of the prism material relative to the liquid, and state whether the absolute refractive index of the prism has changed.
What to remember before solving Refraction Prism questions
Which Refraction Prism formulas do you need for NEET?
1 formula — click to collapse
Prism minimum deviation formula
At minimum deviation (i1 = i2), refractive index from prism angle A and minimum deviation delta_m.
| Symbol | Quantity | SI Unit |
|---|---|---|
| n | refractive index | - |
| A | prism angle | rad |
| delta_m | minimum deviation | rad |
Valid when
- At minimum deviation only
- Symmetric ray path
Where do students lose marks on Refraction Prism?
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
1 item — click to collapse
Category: Negative Marking
Multi-step prism problem combining angle of incidence, refraction (Snell at each face), and minimum deviation formula. Each sin/sin⁻¹ inversion or angle-mode (deg vs rad) confusion compounds.
When it triggers
Prism problem with refractive index, prism angle A, angle of incidence i.
How to avoid
Use sequential angle bookkeeping: at first face, n sin(r1) = sin(i1); at second face, similar; r1 + r2 = A. Compute deviation δ = (i1 + i2) − A. Plug into minimum-deviation formula only when symmetric (i1 = i2).
More in Optics: 8 exam traps and mistakes · 10 formulas · 6 question patterns from its other lessons.
Refraction Prism questions from past NEET papers
1 question from NEET 2021. Answers verified against NTA official keys. — click to collapse
NEET 2021
Find the value of the angle of emergence from the 3 prism. Refractive index of the glass is . 60°
190°
260°
330°
445°
NTA Answer: Option 2(final)
How does NEET ask about Refraction Prism?
1 recurring pattern from past papers — click to collapse
Prism minimum deviation formula. Small-angle approximation also used.
Multi StepMedium
Common distractors
forgets small angle approx
Uses full formula when only A is given
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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