4 )Imagine that you have purchased an inexpensive diffraction grating from Edmun

Question

4 )Imagine that you have purchased an inexpensive diffraction grating from Edmund cientific that is ruled with 5000 lines/inch. Each of these lines corresponds to a slit in the diffraction grating. You illuminate your grating with a sodium lamp which strongly emits the two sodium-D lines (a1 5890 A and 2-5896 A, remember 1 A-1 x 10 10 m). a) The distance between the slits in this grating is b) The more intense D line at 5890 A is diffracted at m. o when m - 0, at o when m 1, and at o when m 2 c) The maximum value of m is because any larger m value requires the sin0 to be greater than 1. d) The less intense D-line at 5896 A is diffracted at o when m O, at o when m 1, and at o when m 2 e) The angular separation of the two sodium D lines is o when m -O, is o when m 1, and is o when m -2. As you go to higher and higher order spectra (i.e. higher m values), the angular separation of the lines (1) increases, (2) remains the same, or (3) decreases. ) If you had purchased the more expensive 15,000 lines/inch grating from Edmund Scientific, the angular separation of the two sodium D lines in the second order spectrum would have been o which is (1) greater, (2) the same as, or (3) smallr than what ocurred with the less cxpensive grating

Explanation / Answer

The first part can be solved as we know that disthance beteen the slits is given by

D=1/N where N=grating constant

D=1/5000lines/inch =1inch/5000=0.0254/5000=5.08*10^{-6} m

b)We know for more intense wavelength is the high one

D sin theta= m *lambda

For m=0

D sintheta=0 it means sin heta=0

Thus Theta=0o or 180o

For m=1

D sintheta=lambda it means sin heta=1

Thus Theta=90o

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.