Diffraction......need help bad

[percy_07]

Suppose that a single slit diffraction pattern is displayed on a screen. The distance between the first minimum on the left of the screen and the first minimum on the right is 5.4mm. The screen is 0.9m from the slit and the wavlength of light is 546nm. Calculate the width of the slit??

[Kurdt]

Simple case of considering the geometry of the situation. The first minimum will occur as ligh has interfered destructively at the first minimum \Theta_1

thus sin \Theta_1=\frac{\lambda} {b}

Where b is the slit width

[Kurdt]

Ok to find theta is a simple case of geometry. Construct a triangle from the slit to the screen and use the values given to determine the angle of the ray. Once calculated you have lambda so the only thing you don't know is b, which will be the sine of theta divided by lambda.

[percy_07]

could you explain it a little more for me please im still not grasping it 100%.