Is there a theoretical limit to the order of the spectrum one would be able to observe and calculate? Justify your answer mathematically.

Yes, there's a limit

Explanation:

Yes, there's a limit which is set by nλ = 90°, because a transmission grating cannot transmit backwards!

In diffraction gratings, the formula is;

nλ = d sinθ

For the maximum number of orders produced,θ = 90°

Thus;

nλ = d sin(90°)

nλ = d

Hence, nλ < d, or n < d/λ

This will represent the highest order of transmission spectra that is observable.

However, a transmission grating will also be able to produce a reflection spectrum which is generally very dim, and not used much. In this, the orders are numbered from the reflection normal, and also limited to nλ < 90°

scientific laws are the result of testing theories and proving them to be facts.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day