Find Single slit diffraction width

[misunderstood]

Ive been marked wrong but not sure why:

The distance between the first and fifth minima of a single-slit diffraction pattern is 0.400 mm with the screen 41.0 cm away from the slit, when light of wavelength 570 nm is used. Find the slit width.


y=m(theata)D/a

m-order = 5
D-distance from slit to screen = 0.43m
a-slit width = ?
y-distance from centre to minima = 0.000450 m

a=m(theata)D/y

((5)*(560x10^-9)*(0.43))/0.000450 = 2.6755x10^-3

The answer I got is 2.68x10^-3 but it's been marked wrong on the computer, is it me or is the answer correct??

 

[Fightfish]

I assume that by "theata" you actually mean the wavelength lambda.
I don't understand the values that you substitute into the equation; they don't match with the values you provided in the question at all.

 

[misunderstood]

Im sorry the online test changes the values after you repeat the question

Ive changed it:
The distance between the first and fifth minima of a single-slit diffraction pattern is 0.450 mm with the screen 43.0 cm away from the slit, when light of wavelength 560 nm is used. Find the slit width.yes lambda as in wavelenght

 

[Fightfish]

The value that you used is the distance of the 5th maxima from the origin (0th order maxima), and not the distance between the 1st and 5th maximas (or minimas - the distance is the same).
$$y_{5} - y_{1} = 0.400mm$$

$$\frac{5 \lambda D}{a} - \frac{1 \lambda D}{a} = 0.400mm$$
You can do the rest of the math.

 

[misunderstood]

thankyou