Double slit and colored wavelength

[Kris1120]

Homework Statement

White light spans the wavelength range be-
tween about 400 nm and 700 nm.
If white light passes through two slits
0.656 mm apart and falls on a screen 1.7 m
from the slits, what is the distance between
the first-order violet and the first-order red
fringes?
Answer in units of mm.

Homework Equations

sin(theta) = m*lambda / d

x = L*tan(theta)

The Attempt at a Solution

I used the first equation to solve for theta for both red light (lambda = 700 nm) which gave theta = .061139 and violet light (lambda = 400 nm) which gave theta = .034936. I used the second equation to plug in theta and solve for x for each of them. I then subtracted the x value of violet from the x value for red and converted to mm. My final answer was 6.781 mm.

 

[alphysicist]

Hi Kris1120,

The Attempt at a Solution

I used the first equation to solve for theta for both red light (lambda = 700 nm) which gave theta = .061139 and violet light (lambda = 400 nm) which gave theta = .034936. I used the second equation to plug in theta and solve for x for each of them. I then subtracted the x value of violet from the x value for red and converted to mm. My final answer was 6.781 mm.

Can you show the steps in how you got 6.781mm? That does not look right to me.

 

[Kris1120]

theta(red) = inverse sin (700 e-9 m / .656 e-3m) = .061139 degrees
x=tan(.061139)*1.7m = .007818

theta(violet)= inverse sin (400 e-9 m / .656 e-3 m) = .034936 degrees
x=tan(.034936)*1.7m = .001037

.007818 - .001037 = .006781 m = 6.781 mm

 

[alphysicist]

theta(red) = inverse sin (700 e-9 m / .656 e-3m) = .061139 degrees
x=tan(.061139)*1.7m = .007818

I'm getting 0.001814 for this. Would you check it again?

 

[Kris1120]

yes! I hate when I do silly things like that! Thank you for correcting me!