Single Slit Exp: Find Number of Minima in 0-19deg Range

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To find the number of minima in a single slit diffraction pattern for a slit width of 819 nm and light wavelength of 405 nm within the angular range of ±19 degrees, the formula tan(theta) = m * (wavelength/slit width) is used. The integer m represents the order of the minima. The values for theta must be converted to radians for accurate calculations. The discussion emphasizes the importance of considering both positive and negative angles when determining the total number of minima. Ultimately, the calculation leads to identifying the specific integer values for m that fit within the given angle range.
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A single slit with width 819 nm is illuminated with light of wavelength 405 nm. How many
minima occur in the angular range from theta = 0 to theta = ±19deg?


I have an exam tomm please help me out with some problems.

actually, i hv the answer but i don't know how to derive it!
 
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i just googled 4 keywords and got the formula, try it! :)
 
Please Help me though!
 
tan(theta) = m * Wavelength/SlitWidth

You know all the values except m.
m is the number of minima (it's an integer obviously).

Be careful about the angle, its a plus-minus.
 

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