Single Slit/Diffraction Problem

[Huskies213]

Homework Statement

A helium neon laser (642nm) illuminates a single slit and is observed on a screen 2.5m behind the slit. The distance between the first and second minima in the pattern is 4.75mm. What is the width of the slit in mm??

Any help here would be greatly appreciated

Homework Equations

w= {2 (lamda) Distance}/ (minima slit distance/distance observed??)

The Attempt at a Solution

w= 2(642x10^-9)(2.5)/(.00475/2.5)

 

[mjsd]

relevant equations:

$$w \sin\,\theta = m\lambda$$ where $$m = 1, 2, 3, \ldots$$, w is the width,
$$\theta$$ is the angle from mid-point of slit to the corresponding position of the minimum.

also for small angle

$$\sin\,\theta \approx \tan\,\theta = \text{vertical displacement}/\text{perpendicular distance to screen}$$; where vertical displacement is the perpendicular distance from the mid-point of slit to the minima. In your case perpendicular distance to screen is given as 2.5m.