Prisms and Dispersion
Tags: #physics #optics #prisms #dispersionEquation
$$\delta=\theta_i+\theta_{i'}+\alpha \\ n=\frac{\sin(\frac{1}{2}(\delta_{\rm min}+\alpha))}{\sin(\frac{1}{2}\alpha)} \\ D=\frac{d\delta}{d\lambda}=\frac{d\delta}{dn}\frac{dn}{d\lambda} \\ \frac{d\delta}{dn}=\frac{2\sin(\frac{1}{2}\alpha)}{\cos(\frac{1}{2}(\delta_{\rm min}+\alpha))}$$Latex Code
\delta=\theta_i+\theta_{i'}+\alpha \\
n=\frac{\sin(\frac{1}{2}(\delta_{\rm min}+\alpha))}{\sin(\frac{1}{2}\alpha)} \\
D=\frac{d\delta}{d\lambda}=\frac{d\delta}{dn}\frac{dn}{d\lambda} \\
\frac{d\delta}{dn}=\frac{2\sin(\frac{1}{2}\alpha)}{\cos(\frac{1}{2}(\delta_{\rm min}+\alpha))}
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Introduction
Equation
Latex Code
\delta=\theta_i+\theta_{i'}+\alpha \\
n=\frac{\sin(\frac{1}{2}(\delta_{\rm min}+\alpha))}{\sin(\frac{1}{2}\alpha)} \\
D=\frac{d\delta}{d\lambda}=\frac{d\delta}{dn}\frac{dn}{d\lambda} \\
\frac{d\delta}{dn}=\frac{2\sin(\frac{1}{2}\alpha)}{\cos(\frac{1}{2}(\delta_{\rm min}+\alpha))}
Explanation
A light ray passing through a prism is refracted twice and aquires a deviation from its original direction.
: is apex angle
: is the angle between the incident angle and a line perpendicular to the surface
: is the angle between the ray leaving the prism and a line perpendicular to the surface
: is refractive index of the prism
: is dispersion of a prism
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