Why Is My Calculation of Slit Width Using Light Diffraction Incorrect?

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The calculation of slit width using light diffraction is incorrect due to misunderstanding the angle measurement. The angle given, 51.5°, represents the separation of dark bands, requiring the angle to be halved for individual band calculations. The correct formula to use is sin(θ) = λ/w, where θ should be 25.75° (51.5°/2). Using this corrected angle, the width of the slit can be accurately determined. Properly applying the angle in the formula is essential for obtaining the correct result.
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1. When blue light of wavelength 450 nm falls on a single slit, the first dark bands on either side of center are separated by 51.5°. Determine the width of the slit.




2. sin\theta=\lambda/w



3. w=450e-9/sin(51.5)=5.75x10-7
I tried this but it said it was wrong, if anyone could help that would be great.
 
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In the problem the given angle is the separation dark bands on either side.
So θ = 51.5/2 degrees.
 

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