1. Jul 23, 2007

### slyman

Two narrow slits of width a are separated by center-to-center distance d. Suppose that the ratio of d to a is an integer d/a=m.

Show that in the diffraction patterns produced by this arrangement of slits, the mth interference maximum (corresponding to dsin(theta)=m$$\lambda$$) is suppressed because of coincidence with a diffraction minimum. Show that this is also true for the 2mth, 3mth, etc., interference maxima.

My attempt dsin(theta)=m$$\lambda$$ indicates the conditions for interference maxima, where d is the distance between the two slits. We know that diffraction minimum occurs when a*sin(theta)=$$\lambda$$, where a is the slit width. Divide by both equations and we can determine which interference maximum coincides with the first diffraction minimum: d/a=m

Last edited: Jul 23, 2007
2. Jul 23, 2007

### Gokul43201

Staff Emeritus

3. Jul 23, 2007

### slyman

My bad. It's just that this question pisses me off.

4. Jul 23, 2007

### Gokul43201

Staff Emeritus
Okay, you've almost answered the first part of the question, but you've gone about it backwards.

Let $d\cdot sin\theta = m \lambda$ and $d/a=m$, then you can show that $a \cdot sin \theta = (d/m)sin \theta =...$..which answers the first part of the question.

For the second part, how would you proceed?