Distance between adjacent fringes

[chef99]

Homework Statement

Light from a laser with a wavelength of 760nm is directed at diffraction grating of 1500 lines/cm. If the diffraction grating is located 15.m from the screen, calculate the distance between adjacent bring fringes.

Homework Equations

∆y = L λ/d

The Attempt at a Solution

Given:

Line density = 1500lines/cm

L = 1.5m

λ = 760nm = 7.6 x10^-7m

Required: ∆y

Solution:

d= 1.0cm / 1500lines

d= 6.67 x10^-6m∆y = L λ/d

∆y = (1.5m)(7.6 x10^-7m) / (6.67 x10^-6m)

∆y = 0.1709m

∆y = 1.7 x10^-1mTherefore, the distance between adjacent bright fringes is 1.7 x10^-1m.

I'm pretty confident with this answer, but I'm not sure if I determined the value of d correctly, (is it always 1.0cm/# of lines?) Also should the final answer be presented as 1.7 x10^-1m, or 0.1709m, as it is not a very small number, as is usually the answer (such as 1.7 x10^-6). Any feedback would be a big help.

 

[BvU]

Hi chef,

You say 1.5 m, the problem statement says 15. m ?

All givens are in two digits, so the answer is too: 0.17 m

 

[chef99]

Hi chef,

You say 1.5 m, the problem statement says 15. m ?

All givens are in two digits, so the answer is too: 0.17 m

Sorry my mistake, it is in fact 1.5m. I just wrote out the problem incorrectly. assuming L= 1.5m, everything else looks good?

 

[BvU]

Looks good, yes.
It is indeed not a small angle. If you want detail: the proper equation is $d\sin\theta = n\lambda$ and $y = L\tan\theta\;.\$ So maxima are at 0, 0.172, 0.351, 0.546, 0.769, 1.041 m from the axis. But the exercise doesn't ask for that kind of detail.