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A polariscope consists of a plane light (Figure 2(a)), a linear polarization filter denoted “polarizer” (b), an optional λ/4-wave plate (c), the object to analyze (d), another optional λ/4-plate (e), another linear polarization filter denoted “analyzer” (f), and the observer or optical acquisition device (g). In a circular polariscope, both λ/4-plates are present, whereas they are missing in a plane polariscope. A wave plate causes a retardation, i.e., a lower speed of light, on the

light components oriented along its “slow” direction (blue arrows in Figure 2), whereas components along its “fast” direction are less retarded. This results in a phase shift of the slow component relative to the fast component. A λ/4-

plate causes a phase shift of p/2, producing circularly polarized light from linearly polarized light. Hence, the linear polarization filter (b) together with the wave plate (c) can be subsumed as a circular polarization filter (circular polarizer),

and the wave plate (e) together with the analyzer (f) as a second circular polarization filter. In a circular polariscope, the two wave plates are oriented perpendicular, i.e., with opposite fast and slow directions (Bußler 143).

Results

Type of Calculation

FEA

Hand

Experimental

Max Stress-σ (psi)

12,101

11,239

7906.8

Percent Error to FEA

0%

7.123%

34.660%

From FEA analysis, σMAX=12,101 psi. From the hand calculations σMAX=11,239 psi. From experimental method, σMAX=7906.8 psi. A high percentage error occurs for the experimental calculation. Reasons include inaccuracies in recording data, human error, and imperfections in the specimen tested.

*Refer to the last section in the Appendices for Results using MathCad*

Discussion

Computer software such as Simulation Mechanical makes engineering more practical in design and testing. Relying solely on computers to run calculations is not enough though. One must understand how equations are being applied to different stress situations. FEA is much more time saving and accurate if you set up your model correctly. The percent error for the hand calculations was fairly small at 7.1% whereas the percent error for the experimental method proved to be very high at 34.6%. Such a large error doesn’t correspond to the other two methods and proves that human error was to blame.

References