# Diffraction grating and wavelengths

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
Homework Helper

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.

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

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
Homework Helper

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

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

rl.bhat
Homework Helper

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

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
Homework Helper

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.

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?

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.

Last edited:
rl.bhat
Homework Helper

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.