Question

A mineral under crossed nicols displays second order greenish-yellow (\(M = 740\) nm) interference colour. On introduction of a gypsum plate (\(A = 550\) nm) along the length of the mineral orientation, first order grey interference colour is displayed. The net retardation is _________ nm (answer in integer).

Hint:

Compare the mineral's own retardation with the gypsum plate's retardation; a large drop in order means the two subtract.

Answer 1

Correct Answer: 190

Step 1: Recall how accessory plates change retardation.
A mineral grain under crossed nicols shows an interference colour that depends on its own retardation, here \(M = 740\) nm (second order greenish yellow). Adding an accessory plate like gypsum (retardation \(A = 550\) nm) either adds to or takes away from this retardation, depending on how the plate's slow direction lines up with the mineral's own vibration directions.

Step 2: Decide whether the plate adds or subtracts.
If the two slow directions are parallel, the retardations add, and the colour should jump to a higher order. If the two slow directions are opposed (one plate's slow direction lines up with the other's fast direction), the retardations subtract.

Step 3: Match the observed result to subtraction.
Here the colour drops all the way down to first order grey, which sits very close to zero retardation on the Michel-Levy chart. A drop this large can only happen if the gypsum plate's retardation is being taken away from the mineral's retardation, not added to it.

Step 4: Calculate the net retardation.
\[ \Delta_{net} = |M - A| = |740 - 550| = 190 \text{ nm} \]

Final Answer:
\[ \boxed{190 \text{ nm}} \]