Prism Deviation Calculator

Q: What is minimum deviation?

For each prism angle, there is a specific angle of incidence where deviation is minimum. At this point the refracted ray is parallel to the base.

Q: How is n measured using a prism?

Measure minimum deviation D_m and prism angle A. Then n = sin((A+D_m)/2)/sin(A/2). Accurate to 5 decimal places with good equipment.

Q: What is angular dispersion?

Different wavelengths have different n, so D_m differs for each color. dD/dlambda = angular dispersion, giving rainbow spread.

Q: What is chromatic aberration in prisms?

Variation of deviation with wavelength. Blue deviates more than red (n_blue > n_red for normal glass). Causes spectrum spread.

A prism deviates light due to refraction at two surfaces. At minimum deviation, the ray passes symmetrically through the prism. This condition is used to precisely measure refractive index.

🌈 Optics📐 D = (A+Dₘ)🔬 Dispersion

Prism Angle A (deg)

Refractive Index n

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Minimum Deviation	D_m	Snell law at both surfaces	deg
Refractive Index	n	n = sin((A+D_m)/2) / sin(A/2)	—
Prism Angle	A	Apex angle of prism	deg
Deviation from n and A	D_m	Solve: n = sin((A+D)/2)/sin(A/2)	deg

Step-by-Step Examples

Example 1

Glass Prism

A=60 deg, n=1.5.

sin((60+D)/2) = 1.5*sin(30) = 0.75
(60+D)/2 = arcsin(0.75) = 48.59
D = 2*48.59 - 60 = 37.2 deg

✓ Minimum deviation = 37.2 deg

Example 2

Dense Flint Glass

A=60 deg, n=1.7.

sin((60+D)/2) = 1.7*sin(30) = 0.85
(60+D)/2 = 58.21, D = 2*58.21-60 = 56.4 deg

✓ 56.4 deg deviation for dense flint glass

Example 3

Measure n from D

Glass prism A=45 deg, measured D_min=25.4 deg.

n = sin((45+25.4)/2)/sin(45/2)
n = sin(35.2)/sin(22.5) = 0.576/0.383 = 1.504

✓ n = 1.504 — typical crown glass

Real-World Applications

🌈

Spectroscopy

Prisms disperse light into spectrum. Different wavelengths deviate by different amounts (dispersion).

🔬

Refractive Index Measurement

Minimum deviation method precisely measures n to 5+ significant figures.

📷

Camera Prisms

Pentaprisms in SLR cameras use TIR to flip the image correctly for the viewfinder.

🔪

Periscopes

Dove prisms and right-angle prisms redirect beams in military and optical instruments.

Common Mistakes to Avoid

⚠️

Minimum deviation is a specific condition

D_min occurs when the ray passes symmetrically through the prism. At other angles, deviation is larger.

⚠️

A must be in degrees, not radians

Formula sin((A+D)/2)/sin(A/2). All angles in degrees. Convert to radians for calculation.

⚠️

n must be greater than 1

Refractive index of the prism must exceed the surrounding medium (typically air, n=1). If n<1, formula fails.

Frequently Asked Questions

What is minimum deviation? ▾

For each prism angle, there is a specific angle of incidence where deviation is minimum. At this point the refracted ray is parallel to the base.

How is n measured using a prism? ▾

Measure minimum deviation D_m and prism angle A. Then n = sin((A+D_m)/2)/sin(A/2). Accurate to 5 decimal places with good equipment.

What is angular dispersion? ▾

Different wavelengths have different n, so D_m differs for each color. dD/dlambda = angular dispersion, giving rainbow spread.

What is chromatic aberration in prisms? ▾

Variation of deviation with wavelength. Blue deviates more than red (n_blue > n_red for normal glass). Causes spectrum spread.

What is an achromatic prism? ▾

Two prisms of different glasses combined to cancel chromatic dispersion while still deviating the beam. Used in binoculars and periscopes.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

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