Giancoli: Wave Nature of Light: Parallel Crests 2.5cm Apart

[leolaw]

This question is related to the wave nature of light from Giancoli:

Water waves having parallel crests 2.5cm apart pass through two openings 5cm apart in a board. At a point 2.0m beyond the board, at what angle relative to the "straight-through" direction would there be little or no wave action?

The reason I am having a problem with this question is because I cannot visualize what a "parallel crest watever wave" is. Is it like the one in this picture (http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/imgpho/sinslitwid.gif) ?

 

[jdavel]

Yes, those are paralllel crests.

 

[leolaw]

how can i find the wavelength of the water wave?
Is it simply just 1/2.5cm or 40m?

 

[jdavel]

what's the definition of wavelength?

 

[leolaw]

distance from crust to crust, gottcha

 

[leolaw]

I find the angle to be 14.48 degree, but I didn't use the 2 meters that the question provdied. Am I missing something?

I use $$d sin (\theta) = (m + \frac {1}{2} )(0.025m)$$ where d = 0.05m, and m = 0 to find $$\theta$$.

 

[OlderDan]

I find the angle to be 14.48 degree, but I didn't use the 2 meters that the question provdied. Am I missing something?

I use $$d sin (\theta) = (m + \frac {1}{2} )(0.025m)$$ where d = 0.05m, and m = 0 to find $$\theta$$.

Since the problem asked you for the angle, and not a distance from the midpoint, you do not need the 2m as long as that distance is much greater than a wavelength. If the distance were only a couple of wavelengths, the approximations used to derive the equation you used would not be justified. Look carefully at this diagram and you will see that there are two angles $\theta$ and $\theta^\prime$ that are only approximately equal.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html