The Diffraction Grating (Grade 12 Physics)

[EmilyBergendahl]

Homework Statement

Do the maxima created by a diffraction grating all have the same intensity? Explain.

Homework Equations

mλ = wsinθ (?)

The Attempt at a Solution

According to the back of my textbook (Nelson Physics 12), the answer is no. I believe the answer may have to do with the fact that a diffraction grating also produces secondary maxima of a lesser intensity than the principal maxima, but I'm not sure. Overall, I would like to understand how to better explain this.

Any help is appreciated!

 

[drvrm]

According to the back of my textbook (Nelson Physics 12), the answer is no. I believe the answer may have to do with the fact that a diffraction grating also produces secondary maxima of a lesser intensity than the principal maxima, but I'm not sure. Overall, I would like to understand how to better explain this.

When in labs (optics with spectrometer) i recall doing the experiment (long back in 1962) i remember that the central maxima was brightest(undiffracted) and the different order of spectra on the right and left of the central beam as
the first order was bright (about 80% intense) and
the 2nd order was less intense say about fifty percent of the first order
the 3rd order was very feeble say about 50% of the 2nd order...the higher orders were not available as the angular position was out of reach.
so, if you plot the intensity/compare it ..its a fact that different order of the diffracted maxima has decreasing intensity and to raise the general intensity the incoming beam was adjusted so that it covers more area of the grating.
naturally a question comes to our mind - what is the reason for this variation-
If one starts with single slit diffraction- the central maxima lies at zero degree, and its maximum intense the secondary maxima and further on are reduced in Intensity- as we add number of slits a theoretical estimate of the Intensity can be done by using superposition principle and it comes out that the diffracted secondary maximas superposed on individual slit diffraction will have reduced intensity and N-slits (grating is a device to raise the intensity of higher order spectral lines) and is used for measurement of lines of different wavelengths-say in sodium light the doublet separation increases as the order of spectra is increased and one can measure closely spaced emission characteristic wavelengths say in hydrogen or helium /mercury/neon spectra.
However the relative intensity of different orders of spectra decreases.
For the expression of Intensity of different orders one can look up
REF.
<https://www.uAlberta.ca/~pogosyan/teaching/PHYS_130/FALL_2010/lectures/lect36/lecture36.html>