m\Delta\lambda = d sin(\Delta\alpha)

mit:
\Delta\lambda = 300nm
\Delta\alpha = 20°
m = 1

\lambda_1=d*sin(\theta)
\lambda_2=d*sin(\theta+\Delta\theta)

sin(x_1+x_2)=sin(x_1)cos(x_2)+sin(x_2)sin(x_1)
mit 
x_1=\theta
x_2=\Delta\theta

sin(\theta)=\lambda_1/d

1=sin(\theta)^2 + cos(\theta)^2

umgeformt nach cosinus

cos(\theta)=sqrt(1-sin(\theta)^2)

d=sqrt(((\lambda_2 - \lambda_1*cos(\Delta\theta))^2/sin(\theta)^2 + \lambda_2^2