when theta is small,we often use the \"small-angle approximation\": we use just

Question

when theta is small,we often use the "small-angle approximation": we use just theta [in radians] in place of sintheta or tantheta. Since the three are very nearly equal in the table bellow. Calculate let the values and percentage error we would get by useing theta in radiens in place of sintheta or tantheta.(you do not need to show your work. use as many significant figures as necessary to see a difference-more sig figs will be needed for smaller angles. as an example, one line of the table is completed for you.) you notice a thin layer of oil floting on the surface of a water puddle. suppose that sunlight strikes the puddle nearly directly over head, and also that you are viewing the puddle from nearly directly above the paddle. you see several different regions of bright colour reflected fom the oil - the colour veries as the oil's thickness varies. in one particular region, the oil appears to be bright green (lamda

Explanation / Answer

.1o  in radians = .00174532925

sin(.1) = .00174532836 and percent error = .000051%

tan(.1) = .00174533102 and percent error = .0000010%

10o in radians = .174532925

sin (10) = .1736481777 and percent error = .507%

tan (10) = .176326981 and percent error = 1.03%

30o in radians = .523599

sin (30) = .5 and percent error = 4.51%

tan (30) = .57735 and percent error = 10.3%

Number 4)

Apply 2nt = (m+.5)(wavelength)

(2)(1.6)(t) = (m+.5)(555 X 10-9)

For m = 0, t = 86.7 nm

For m = 1, t = 260.2 nm

For m = 2, t = 433.6 nm

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