The # of bright fringes in a double slit with finite width?

[Plana]

Homework Statement

Laser light with a wavelength 633 nm is used to illuminate two slits separated by 0.125 mm. The width of each slit is 0.0150 mm. Assuming that only fringes between the first minima in the pattern are counted, how many bright fringes are visible?

lambda = 633nm
d = 0.125mm
w= 0.0150mm

Homework Equations

# of bright fringes visible = 2(d/w)-1

or

m = d/w

The Attempt at a Solution

I tried to use the first formula for the solution

2(d/w)-1

2(0.125/0.015)-1 = 15.67

therefore, 15 bright fringes are visible.

However, the solution manual for my textbook says to use m=d/w
which results in m=8. Therefore there are 2(8)+1 = 17 bright fringes visible. [/B]
I don't see how this is correct because the question asks for the # of visible bright fringes. Since the bright fringes at the end are not visible because they overlap the first order dark fringes. Can anyone clarify this for me?


Sorry if my post is formatted incorrectly... First time using this website.

 

[blue_leaf77]

See this post https://www.physicsforums.com/threads/slit-sizes-needed-for-light-diffraction.831033/#post-5224701.

 

[J Hann]

I would tend to agree with your reasoning since
sin (theta) = lambda / w for the angle to the first single slit minimum
Plugging this into
m = d sin (theta) / lambda does give you d/w for 8 bright fringes on either side

 

[blue_leaf77]

m = d sin (theta) / lambda does give you d/w for 8 bright fringes on either side

Don't forget the central bright fringe.