Question 3

n(λ) = αλ + β/λ². Minimize: dn/dλ = α − 2β/λ³ = 0 → λ³ = 2β/α = 2(0.096)/3 = 0.064 → λ = 0.4 μm. n = 3(0.4) + 0.096/0.16 = 1.2 + 0.6 = 1.8. D_m = (n−1)A = 0.8 × 6° = 4.8°.

**Calculating dimensions and JSON** I need to solve this straightforward problem. I have n = 3λ + .096/λ² to minimize. It leads me to λ³ = .192/3, which gives me λ = .064 or .4 micron. After that, I find n1 as 1.2 + .6 = 1.8. Also, I have D = .8 * 6, resulting in 4.8 B. My next goal is to finalize the JSON for this, ensuring it meets the user's expectations, which seem to be somewhat ambiguous. Let’s get that JSON ready!

No written reasoning was returned for this item.

Minimizing n(λ) by setting the derivative to zero gives λ³=2β/α, and plugging in α=3 and β=0.096 yields λ=0.4 μm, so n at this wavelength equals 1.8. Now I'm computing the prism deviation using D=(n-1)*A.