Diffraction grating and wavelengths

[dimpledur]

diffraction grating URGENT

Homework Statement

A spectrometer is used to analyze a light source. The screen-to-grating distance is 50.0 cm and the grating has 5000 slits/cm. Spectral lines are observed at the following angles: 12.98, 19.0, 26.7, 40.6, 42.4, 63.9 and 77.6. How many different wavelengths are present in the spectrum of this light source? FInd each of the wavelengths.

Homework Equations

d*sinthetha =m*lambda

d=0.0002cm

The thing I am really confused about is the value "m". Which values would I use for this question, because I know m=0,+/-1,+/-2 etc..

I just don't understand which values to use.

The Attempt at a Solution

 

[rl.bhat]

Find the sin( theta) of all the angles.
For same d and lambda, some sin(theta) must be equal to m*sin(12.98). Find m values. Repeat the same thing for other wavelengths.

 

[dimpledur]

since there are 7 different angles, does that mean there will be seven different wavelengths?

 

[dcramps]

Find the sin( theta) of all the angles.
For same d and lambda, some sin(theta) must be equal to m*sin(12.98). Find m values. Repeat the same thing for other wavelengths.

I do not understand what you are trying to say here.

I know d, I do not know λ or m. How can I solve for two unknowns here? Your statement is very confusing.

 

[rl.bhat]

No. Not necessarily. Find the sine of all angles.

 

[dimpledur]

I still don't really understand how to find the values of m.. For some reason this is really confusing

 

[rl.bhat]

Will you please write down sine values of all the angles. Then I will tell you how to find m.

 

[dimpledur]

sin12.98=0.2246
sin19=0.3257
sin26.7=0.4493
sin40.6=0.6508
sin42.4=0.6743
sin63.9=0.8980

 

[rl.bhat]

sin12.98=0.2246
sin19=0.3257
sin26.7=0.4493
sin40.6=0.6508
sin42.4=0.6743
sin63.9=0.8980
These four belong to the same wavelength. Because other three are multiple of 0.2246. And the remaining two belong to another wavelength.

 

[dimpledur]

sin12.98=0.2246
sin19=0.3257
sin26.7=0.4493
sin40.6=0.6508
sin42.4=0.6743
sin63.9=0.8980
These four belong to the same wavelength. Because other three are multiple of 0.2246. And the remaining two belong to another wavelength.

Alright, so there is a total of 3 different wavelengths? I think I got that.

However, when calculating the wavelengths, would sin12.98, have m=1
would sin 19 have m=1 too?
same goes for sin40.9, m=1?

 

[dcramps]

Sorry for intruding here again (I am working on the same problem) but I think that 12.98/19=1, 26.7/40.6=2, 42.4/77.6=3 and 63.9=4

?


edit: I have checked it out, and as far as I can tell this is correct.

 

[rl.bhat]

Alright, so there is a total of 3 different wavelengths? I think I got that.

However, when calculating the wavelengths, would sin12.98, have m=1
would sin 19 have m=1 too?
same goes for sin40.9, m=1?

For last one m = 2
And for 77.6 degree, m=3.