# Finding Expected Lateral Displacement From a Risley Prism

1. Sep 16, 2014

### Pythia

1. The problem statement, all variables and given/known data
Find the expected lateral displacement for a spot of light at a power of $6^{∆}$.

Distance from prism to where displacement was measured (b) = 62.2cm.

The following displacements (x) were measured from the power given on the knob of the prism:

$3^{∆}$ = 1.80cm
$6^{∆}$ = 3.51cm

2. Relevant equations

P = 100$\frac{x}{b}$

If prisms are at 90° to each other, then resulting power will be 2P (with appropriate displacement). If prisms are at any other angle [0°,90°) then resulting power is 2Psinθ where θ is the angle between the two prism.

3. The attempt at a solution

$6^{∆}$ = 100$\frac{x}{62.2cm}$

x = 3.73cm

This is comparable to what I recorded, however I'm unsure then why I was told to record the $3^{∆}$ reading and if the 2P or 2Psinθ parts were needed.

2. Sep 16, 2014

### BvU

Hello Pythia, and welcome to PF.
Am I right in reading $6^{∆}$ as $6^\circ$ (six degrees) ?

It is rather difficult for an outsider to get an idea of what this is about. Could you post some more info, and perhaps a sketch of the situation ?