Physics Introductory Diffraction Pattern Problem

[RandallK]

Homework Statement

Light of wavelength 588 nm illuminates a single 0.70 mm wide slit. At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 1.82 mm from the central maximum?

Homework Equations

Im not sure on the equation, someone told me you need to find the angle. The formula for the angle is: a*sin(theta)=lambda. A being the width of the slit, and Lambda being the wavelength.

The Attempt at a Solution

However if I plug that in I get the angle as .0483. I solve for the angle by: .00059 mm/ .70 mm =8.429 E^-4. Sin^-1(8.429 E^-4) =.0483. I don't see how the angle could be .0483 and I am not sure what the next step is after.

Thanks for any help in advance.

-Randall

 

[haruspex]

I solve for the angle by: .00059 mm/ .70 mm =8.429 E^-4. Sin^-1(8.429 E^-4) =.0483.

You must have keyed the digits in in the wrong order. For such small angles, sin theta is almost the same as theta.
Draw a diagram. The relationship between theta, the distance to the screen and the distance from centre to first minimum on the screen should be obvious.