Question

If the indices of refraction of a uniaxial section are \(\epsilon = 1.653\) and \(\omega = 1.544\), and the retardation between the two rays is 550 nm, then the thickness of the section is ________ µm. (Round off to two decimal places.)

Hint:

Use \( t = \frac{\text{Retardation}}{\epsilon - \omega} \). Convert nanometers (nm) to micrometers (µm): 1 µm = 1000 nm.

Answer 1

Correct Answer: 5

Step 1: Formula used.
\[ \text{Retardation} = t (\epsilon - \omega) \] where \( t \) = thickness, \( \epsilon \) = extraordinary refractive index, \( \omega \) = ordinary refractive index.
Step 2: Substitute known values.
\[ 550 \, \text{nm} = t (1.653 - 1.544) \] \[ t = \frac{550}{0.109} = 5045.9 \, \text{nm.} \] Step 3: Convert to micrometers.
\[ t = 5045.9 \, \text{nm} = 5.05 \, \mu\text{m.} \] Step 4: Conclusion.
Thickness of section = 5.05 µm.