# Spectrometer Experiment > Spectrometer experiment for JEE Physics: minimum deviation δm = 2i − A, n = sin((A+δm)/2)/sin(A/2), sodium D lines and the i–δ curve reasoning. - Canonical URL: https://prepelephant.com/topics/jee/physics/spectrometer-experiment-jee - Exam / course: JEE · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Spectrometer Experiment", PrepElephant, https://prepelephant.com/topics/jee/physics/spectrometer-experiment-jee ## Direct answer Turn the telescope until the coloured image of the slit retreats, hesitates and returns — that turning point is minimum deviation, the condition where light passes symmetrically through the prism (incidence equals emergence, each internal refraction angle equals A/2) and the deviation is δm = 2i − A. The spectrometer's payoff formula follows from Snell's law applied to either face: n = sin((A + δm)/2)/sin(A/2), the refractive index of the prism material from two measured angles alone. The instrument itself is a collimator (slit plus lens, delivering parallel light), a prism table and a telescope, each with its adjustment ritual, and its circular vernier scales (least count commonly one minute of arc) deliver the angular bookkeeping. Measured with a sodium lamp, the prism splits the yellow light into the D doublet at 589.0 and 589.6 nm — two lines resolvable on a well-adjusted instrument. ## What you must remember - **Minimum deviation condition:** the ray traverses symmetrically, i = e and r1 = r2 = A/2; deviation δm = 2i − A, the minimum of the i–δ curve. - **The index formula:** n = sin((A + δm)/2)/sin(A/2); everything reduces to measuring A and δm accurately. - **Small-angle limit:** for a thin prism, δ = (n − 1)A — deviation independent of the angle of incidence, the thin-lens-like simplification. - **Instrument anatomy:** collimator produces parallel light; telescope focused for parallel rays (adjusted to infinity on a distant object or by autocollimation); prism table levelling screws set the principal section vertical. - **Angle of the prism:** measured by reflecting light from both polished faces in turn; the angle between the two telescope positions equals 2A. - **Why minimum is findable:** the i–δ curve is U-shaped with a flat bottom, so the image seems stationary near minimum — the experimental reason the reading is sharp. - **Sodium D doublet:** 589.0 and 589.6 nm, the standard calibration light of the optics laboratory; dispersion is why the prism (unlike a mirror) needs monochromatic light for a clean index value. ## The minimum deviation measurement Do the arithmetic of the standard observation: an equilateral prism, A = 60°, with minimum deviation measured at δm = 40° using sodium light. Then n = sin((60 + 40)/2)/sin(60/2) = sin50°/sin30° = 0.766/0.5 = 1.532 — a typical crown glass. One more step yields the critical angle: sin C = 1/n = 0.653, C ≈ 40.8°, which is why a 45°-45°-90° prism of this glass totally internally reflects at its hypotenuse — the prism periscope and binocular design standing on this very measurement. The experiment's sequence trains the reasoning the exams probe. Telescope to infinity first; collimator slit sharpened; prism set with its refracting edge toward the collimator. Swing the telescope to the deviated image and rotate the prism table so the deviation shrinks: the image drifts with you, then hesitates and returns — that stationary point is δm, read on both verniers and repeated on the other side of the direct view. Reflections off the two polished faces give the prism angle A. Errors students actually make are procedural: an un-levelled table tilts the principal section, and a single vernier leaves eccentricity error uncorrected — hence two verniers 180° apart, read and averaged every time. ## Exam framing of the experiment JEE has a stable set of interests here. The i–δ graph: a U-shaped curve whose minimum corresponds to symmetric passage — a "match the column" staple pairing graph regions with ray diagrams. Second, the formula manipulation: given n and A, invert to find δm (sin((A + δm)/2) = n sin(A/2)), or compare two glasses by their δm. Third, conceptual: why is the measurement made at minimum deviation rather than anywhere else? Because the geometry is symmetric, the emergent ray is best defined, the sensitivity of δ to small i-errors is least (the flat bottom), and the formula simplifies. Fourth, thin-prism questions: δ = (n − 1)A constant for all incidence angles — the small-angle escape from the whole derivation. Fifth, dispersion: violet bends more than red (n_violet > n_red), so the prism spreads white light while a mirror never would; angular dispersion (n_v − n_r)A attaches here. Main tests the formula and graph; Advanced adds the grazing-incidence or grazing-emergence extremes of the same curve, where δ approaches its maximum. ## Frequently asked questions ### What is the condition for minimum deviation through a prism? The ray passes symmetrically: angle of incidence equals angle of emergence, and inside the glass both refraction angles equal A/2, making the total deviation δm = 2i − A. ### How is refractive index found from the spectrometer readings? Through n = sin((A + δm)/2)/sin(A/2), using the measured prism angle A and minimum deviation δm — two angles yield the index. ### Why is the refractive index measured at minimum deviation and not elsewhere? Because the deviation there is stationary (insensitive to small setting errors), the passage is symmetric so formulas simplify, and the emergent image is sharpest for the reading. ### What does the i–δ curve for a prism look like? A U-shaped curve: deviation falls as incidence rises, flattens at the minimum, then climbs again — the flat minimum is what makes the experiment precise. ### What is the small-angle prism approximation? For small prism angles δ = (n − 1)A, independent of the angle of incidence — the basis of thin prisms used in rangefinders and optical instruments.