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Prism Deviation: Angle of Deviation and Minimum Explained

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When light passes through a prism it changes direction. The total change is the angle of deviation. As you vary incidence angle, deviation first decreases, reaches a smallest value, then increases. This minimum deviation position is special and highly useful.

Understanding this curve helps measure refractive index with high accuracy and explains symmetric ray passage. It is a favourite experiment in school labs because the minimum is easy to locate precisely.

Key Concepts

Angle of deviation D: Angle between incident ray extended and emergent ray, degrees.

Minimum deviation Dm: Smallest possible deviation for given prism and colour, occurs when ray passes symmetrically, i1 = i2 and r1 = r2 = A divided by 2.

Prism angle A: Apex angle between refracting faces, degrees, usually 60 degrees.

  • Graph of D vs i is U-shaped with flat bottom at Dm
  • At Dm, internal ray parallel to base for equilateral prism
  • Dm larger for violet than red because n larger

Formulas

D = i1 + i2 minus A, and r1 + r2 = A. i1, i2 incidence and emergence angles, r1, r2 internal refraction angles.

At minimum: n = sin((A + Dm) divided by 2) divided by sin(A divided by 2). n dimensionless, angles degrees. Assumes monochromatic light, prism in air.

Also i1 at minimum = (A + Dm) divided by 2.

Worked Example

A prism A = 60 degrees gives Dm = 40 degrees for a colour. Find refractive index and incidence angle at minimum.

  1. Compute (A + Dm) divided by 2 = (60 + 40) divided by 2 = 50 degrees, sin = 0.7660.
  2. sin(A divided by 2) = sin 30 degrees = 0.5.
  3. n = 0.7660 divided by 0.5 = 1.532.
  4. Incidence at minimum i = (A + Dm) divided by 2 = 50 degrees, same as emergence.

If measured Dm were 42 degrees for violet, n would be sin 51 degrees divided by 0.5 = 0.777 divided by 0.5 = 1.554, slightly higher, showing dispersion.

Common Misconceptions

  • Deviation minimum zero: Even at best symmetric passage, prism still bends light towards base, Dm is typically 37-40 degrees for glass equilateral.
  • Any incidence gives same deviation: Deviation larger at grazing or steep angles, only one i gives minimum (two i values give same D except minimum).
  • Dm same for white light: White gives range, each colour has its own Dm. Yellow often taken as mean.

Real-World Applications

  • Refractive index measurement with spectrometer using Dm is textbook precision method
  • Spectroscopy uses minimum deviation position for stable calibration
  • Prism design for periscopes and optical devices chooses incidence near Dm for minimal distortion
  • Understanding D vs i curve helps align optical instruments

Deviation D = i1 + i2 minus A reaches minimum Dm when passage symmetric. That position gives n directly from sin formula and anchors prism experiments.

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