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## Homework Statement

The centres of two slits of width

*a*are a distance

*d*apart. If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light, the ratio a/d is equal to:

ANS: 1/4

## Homework Equations

Here are the various interference conditions for interference and diffraction:

Interference conditions for

*double slit*:

MAX: dsinθ = mλ

MIN: dsinθ = (m+½)λ

Diffraction conditions for a

*single slit*:

MAX: asinθ = (m+½)λ

MIN: asinθ = mλ

Diffraction conditions for

*diffraction grating:*

MAX: asinθ = mλ

MIN: asinθ = (m+½)λ

## The Attempt at a Solution

I will walk through my reasoning...

I've classified the diffraction component of this problem as

*diffraction grating*rather than

*diffraction through a single slit*, because based on this setup, there are two slits for diffraction to occur through. While we normally see grating in the order of 2500grates/cm, 2grates/cm would still be considered grating.

So based on that logic, the conditions for minimum for both are:

Diffraction: dsinθ = (m+½)λ, where m=1

Interference: asinθ = (m+½)λ, where m=4

Now, when I plug in all the values for m, and cancel out all the similarities (sinθ, λ):

asinθ=(1+½)λ --> a=1.5

dsinθ=(4+½)λ --> d=4.5

The ratio I get for a/d = 1.5/4.5 = ⅓

HOWEVER, I noticed that if I cancel out ½ rather than adding it to m like I did above, then the ratio for a/d=¼.

What am I doing wrong?