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

[mustang1988]

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.

 

[rl.bhat]

In the problem the given angle is the separation dark bands on either side.
So θ = 51.5/2 degrees.

 

[kerimek]

I would first like to commend you for your attempt at solving the problem. However, there seems to be a calculation error in your solution. The correct calculation should be w=450e-9/sin(51.5°)=6.5x10-7 meters. This is the width of the slit in meters. It is important to note that the unit for wavelength (nm) must be converted to meters (m) before performing the calculation. Additionally, the angle given in the problem is in degrees, so it is important to convert it to radians by dividing by 180° and multiplying by π. It is always a good idea to double check your calculations and units to ensure accuracy. I hope this helps.