Distance between two bright fringes

[csinger1]

Homework Statement

A new experiment is created with the screen at a distance of 2.2 m from the slits (with spacing 0.12 mm). What is the distance between the second order bright fringe of light with l = 683 nm and the third order bright fringe of light with l = 400 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)

Homework Equations

sin∅=mλ/d

The Attempt at a Solution

For first wavelength,
∅=arcsin(2(683*10^-9)/1.2*10^-4)
∅=.65
Setting up triangle, I get D_683=2.2tan(.65)=.0249

For second wavelength,
∅=arcsin(3(400*10^-9)/1.2*10^-4)
∅=.57
Setting up triangle, I get D_400=2.2tan(.57)=.0219
I thought that D_683-D_400 should give me the distance between the two fringes but my answer of .003m keeps getting rejected. I have done this problem over and over and I cannot for the life of me figure out what I am doing wrong.

 

[Steely Dan]

The math looks pretty solid to me. Not quite sure why that answer would be rejected. Sorry if that's not helpful.

 

[bayan]

Homework Statement

A new experiment is created with the screen at a distance of 2.2 m from the slits (with spacing 0.12 mm). What is the distance between the second order bright fringe of light with l = 683 nm and the third order bright fringe of light with l = 400 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)

Homework Equations

sin∅=mλ/d

The Attempt at a Solution

For first wavelength,
∅=arcsin(2(683*10^-9)/1.2*10^-4)
∅=.65
Setting up triangle, I get D_683=2.2tan(.65)=.0249

For second wavelength,
∅=arcsin(3(400*10^-9)/1.2*10^-4)
∅=.57
Setting up triangle, I get D_400=2.2tan(.57)=.0219
I thought that D_683-D_400 should give me the distance between the two fringes but my answer of .003m keeps getting rejected. I have done this problem over and over and I cannot for the life of me figure out what I am doing wrong.

Might want to find the width of each fringe too, it does state smallest possible value, but with your calculation it is not smallest possible value.