Measure Refractive Index & Study Dispersion Using Minimum Deviation Method
✅ FREE Experiment • 🎨 3D Ray Tracing • 🎓 NEB Class 12 Physics
A Prism Spectrometer is a precision optical instrument used to measure the refractive index of transparent materials and study the dispersion of light. When white light passes through a prism, it splits into its constituent colors (spectrum) because different wavelengths refract by different amounts - a phenomenon called dispersion.
This experiment uses the Minimum Deviation Method to accurately determine the refractive index. At a particular angle of incidence, the angle of deviation becomes minimum. At this minimum deviation position, the ray inside the prism is parallel to the base, and the formula n = sin[(A + D_min)/2] / sin(A/2) gives the refractive index, where A is the prism angle and D_min is the minimum angle of deviation.
🌈 Watch light rays refract through the prism and separate into colors
Typical: 60° (equilateral prism)
Adjust to find minimum deviation
For yellow light (reference)
Where: n = refractive index, A = prism angle, Dmin = minimum angle of deviation
Given: Prism angle A = 60°
| S.No. | Color | Wavelength (nm) |
Angle of Incidence i (°) |
Angle of Deviation D (°) |
Min Deviation Dmin (°) |
Refractive Index n |
|---|---|---|---|---|---|---|
| No observations recorded yet. Select a color and click "Record" to add readings | ||||||
Mean Refractive Index (for yellow): Calculate after recording observations for different colors
The curve shows minimum deviation point. At i = e (symmetric ray path), deviation is minimum.
A prism is a transparent optical element with flat, polished surfaces that refract light. A triangular prism has two refracting surfaces inclined at an angle A (called the prism angle or refracting angle). When light passes through a prism:
The angle between the incident ray direction (extended) and the emergent ray direction is called the angle of deviation (D). It depends on:
As the angle of incidence increases from small values, the deviation first decreases, reaches a minimum value Dmin, and then increases again. This minimum deviation occurs when the ray inside the prism is parallel to the base, and the incident angle equals the emergent angle (i = e). This is called the minimum deviation position.
For any ray passing through a prism:
Where r₁ and r₂ are angles of refraction at first and second surfaces.
When D = Dmin, the ray path is symmetric:
Dispersion is the phenomenon of splitting white light into its constituent colors (spectrum) when passing through a prism. This occurs because:
The variation of refractive index with wavelength is given approximately by:
For most materials in visible range, the first two terms suffice. This shows n decreases with increasing wavelength.
The angular separation between extreme colors (violet and red) in the spectrum is called angular dispersion (θ):
The dispersive power (ω) of a prism material is defined as:
Where nv, nr, ny are refractive indices for violet, red, and yellow light respectively. Yellow (D-line of sodium) is used as the reference wavelength.
Advantages of using minimum deviation position:
| Material | n (yellow light) | Dispersive Power |
|---|---|---|
| Crown Glass | 1.517 | 0.017 |
| Flint Glass | 1.650 | 0.031 |
| Water | 1.333 | 0.013 |
| Diamond | 2.417 | 0.044 |
A prism spectrometer is a precision optical instrument used to measure the refractive index of transparent materials and study the dispersion of light. It consists of a collimator (produces parallel light), a prism table (holds the prism), and a telescope (observes the refracted/reflected light). All components are mounted on a circular graduated scale for angle measurements.
The angle of minimum deviation (Dmin) is the smallest angle of deviation that occurs for a particular prism and wavelength. At this position, the ray inside the prism is parallel to the base, and the incident angle equals the emergent angle (i = e). This position is unique and used for accurate refractive index measurements.
At minimum deviation: i = e and r₁ = r₂ = r
From geometry: A = r₁ + r₂ = 2r, so r = A/2
Also: Dmin = i + e - A = 2i - A, so i = (A + Dmin)/2
Applying Snell's law at first surface: sin(i) = n·sin(r)
Therefore: sin[(A + Dmin)/2] = n·sin(A/2)
Final formula: n = sin[(A + Dmin)/2] / sin(A/2)
Dispersion is the phenomenon of splitting white light into its constituent colors (spectrum) when passing through a prism. It occurs because refractive index varies with wavelength - shorter wavelengths (violet) refract more than longer wavelengths (red). The spectrum order is VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red).
Advantages: (1) High accuracy - near minimum, deviation changes very slowly, so small angle measurement errors have minimal effect, (2) Easy to locate - spectrum/ray reverses direction at this point, (3) Symmetric path - i = e simplifies calculations, (4) Unique value - for given prism and wavelength, Dmin is unique, (5) Simple formula - only need A and Dmin.
Place prism on table, observe refracted spectrum through telescope. Slowly rotate prism table in one direction - spectrum moves in same direction initially. Continue rotating until spectrum stops momentarily, then reverses direction. This reversal point is minimum deviation position. Lock table, measure angles. For precise work, approach from both directions and take mean.
Conditions at minimum deviation: (1) Ray inside prism is parallel to the base, (2) Incident angle equals emergent angle (i = e), (3) Angles of refraction at both surfaces are equal (r₁ = r₂), (4) Ray path is symmetric, (5) dD/di = 0 (deviation is stationary with respect to incidence angle).
Violet light has shorter wavelength (~400 nm) compared to red light (~650 nm). Refractive index decreases with increasing wavelength, so nviolet > nred. Since deviation depends on refractive index, violet deviates more. This wavelength dependence of refractive index is described by Cauchy's equation: n = A + B/λ².
Angular dispersion is the angular separation between extreme colors (violet and red) in the spectrum: θ = Dviolet - Dred. It represents how much the prism spreads out the spectrum. Higher refractive index materials and larger prism angles produce greater angular dispersion.
Dispersive power (ω) is the ratio of angular dispersion to mean deviation: ω = (nv - nr)/(ny - 1), where subscripts v, r, y denote violet, red, and yellow light. It's a material property independent of prism angle. Crown glass has ω ≈ 0.017, flint glass ω ≈ 0.031 (higher dispersion).
(1) Collimator: Contains slit and converging lens to produce parallel light beam, (2) Prism table: Circular rotating table with leveling screws to hold prism, (3) Telescope: For observing refracted/reflected light, contains objective lens and eyepiece, (4) Circular scale and verniers: For precise angle measurements (typically 1' or 30" accuracy).
Method: (1) Remove prism, align telescope with collimator (direct reading), (2) Place prism on table so light reflects from one refracting face, (3) Rotate telescope to see reflected image, note angle θ₁, (4) Rotate telescope to see reflection from other face, note angle θ₂, (5) Prism angle A = (θ₂ - θ₁)/2. The factor 2 comes from angle of reflection equals angle of incidence.
The collimator converts diverging light from the slit into a parallel beam. This is essential because: (1) Snell's law calculations assume parallel rays, (2) All rays have same angle of incidence on prism, (3) Produces sharp spectral lines in telescope, (4) Necessary for accurate angle measurements. The slit is placed at the focal point of collimator lens.
A narrow slit: (1) Produces sharp spectral lines (better resolution), (2) Reduces overlapping of colors in spectrum, (3) Improves accuracy of angle measurements, (4) Acts as line source approximation. However, extremely narrow slits reduce brightness. Typical slit width is 0.01-0.1 mm, adjusted based on light intensity and required resolution.
Spectrum: The band of colors (or wavelengths) produced when light is dispersed, showing the distribution of electromagnetic radiation by wavelength. Spectroscopy: The scientific study of spectra to determine composition, temperature, velocity, and other properties of light sources (stars, lamps, materials). It's a powerful analytical technique used in physics, chemistry, astronomy, and biology.
Rainbows are caused by dispersion and internal reflection of sunlight in water droplets. Process: (1) Sunlight enters droplet and refracts (disperses into colors), (2) Reflects off back surface (total internal reflection), (3) Refracts again on exit, (4) Different colors emerge at different angles (42° for red, 40° for violet), (5) Observer sees circular arc of colors. Double rainbows occur due to two internal reflections (order reversed).