Prism Minimum Deviation

n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}

At minimum deviation, light passes symmetrically through the prism. This formula relates the refractive index to the prism angle and minimum deviation.

Variables

Refractive index

Allowed values: 1 or more

unitless

Prism apex angle

Allowed values: greater than 0

δ_m

Minimum deviation angle

Derivation

At minimum deviation, the ray inside the prism is parallel to the base, and the angles of incidence and emergence are equal.

Your notes

0/5000

Check value

Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

A = 2 ° (Prism apex angle)
δ_m = 3 ° (Minimum deviation angle)

Result: n = 2.4993337

Other optics formulas with the same quantities

Refractive Index (Refraction) shares Refractive index
Apparent Depth (Refraction) shares Refractive index
Optical Path Length (Wave Optics) shares Refractive index

Where this formula is listed

Optics formulas, under Prisms.
In the optics list it comes after Dispersion (Angular).
Optics formula sheet, one of 34 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Prism Minimum Deviation formula?

Prism Minimum Deviation is written n = sin((A + δ_m)/2)/sin(A/2). At minimum deviation, light passes symmetrically through the prism. This formula relates the refractive index to the prism angle and minimum deviation. It belongs to Optics, under Prisms.

What are the units in n = sin((A + δ_m)/2)/sin(A/2)?

In SI units, n is refractive index (dimensionless); A is prism apex angle, measured in °; δ_m is minimum deviation angle, measured in °.

How is the Prism Minimum Deviation formula derived?

At minimum deviation, the ray inside the prism is parallel to the base, and the angles of incidence and emergence are equal. The result is n = sin((A + δ_m)/2)/sin(A/2).