Nebenrechnung zu Aufgabe 5.2 b)

R = (r1^2 + r2^2 + 
            2 r1 r2 Cos[2 π ng d/λ])/(1 + r1^2 r2^2 + 
            2 r1 r2 Cos[2 π ng d/λ])

D[R, λ]

Solve[D[R, λ] == 0, d]

Reduce[D[R, λ] == 0, d]

r2 = (ng - ns)/(ng + ns);

R2 = (r1^2 + r2^2 + 
            2 r1 r2 Cos[2 π ng d/λ])/(1 + r1^2 r2^2 + 
            2 r1 r2 Cos[2 π ng d/λ])

D[R2, ns]

Solve[D[R2, ns] == 0, d]

Reduce[D[R2, ns] == 0, d]