3. Light from an emission line lamp is normally incident on a transmission diffraction grating with 550 lines per mm. What is the diffraction angle 0 (in degrees) for a spectral line with a wavelength of 2 = 565.270 nm observed in second order? а. b. What is the minimum resolution, R, for the above spectral line to be just resolved from another spectral line at 1, = 565.285 nm? How many grooves or lines on the grating must be illuminated in order to achieve the above resolution in second order. С. What minimum size, D, grating (550 lines per mm) is needed to achieve the resolution in part b.) in second order? d.
3. Light from an emission line lamp is normally incident on a transmission diffraction grating with 550 lines per mm. What is the diffraction angle 0 (in degrees) for a spectral line with a wavelength of 2 = 565.270 nm observed in second order? а. b. What is the minimum resolution, R, for the above spectral line to be just resolved from another spectral line at 1, = 565.285 nm? How many grooves or lines on the grating must be illuminated in order to achieve the above resolution in second order. С. What minimum size, D, grating (550 lines per mm) is needed to achieve the resolution in part b.) in second order? d.
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please answer part b, c, and d
Transcribed Image Text:Waves in general:
FORMULA PAGE 1
a y
1-dimensional wave equation:
1 a'y
; here v is the speed of the wave
v? ôt?
Solution: f(x- vt) or f(x+vt)
Harmonic or sinusoidal waves: y(x,t)= Asin(kx- ot)
2л
k
2n
= 27f; v=-
T
v = f2
General Constants:
-34
h = 6.626×10*J.s = 4.13567×10¬eV ·s ; (with recent revisions to the SI system of
units Planck's Constant is defined to have an exact value: h= 6.62607015×10¯“J·s)
–34
-19
hc = 1240 eV · nm; hc=1239.84eV · nm (for more accuracy); leV =1.6022×10-J
= 299,792, 458 m /s (exact);
-31
electron mass: m, =9.1094×10' kg
proton mass: m,
=1.6726×10-27 kg
Photons: E = hf
hc
; Protons: m,c² = 938.3MEV , Electrons: m.c² = 511.0keV
%3|
h
= 1.0546x10 34J•s = 6.5821×10-1eV ·s
Chapter 36. Diffraction
Single slit diffraction:
Minima:
a sin 0, = ma, m=1,2,3,...where a is the slit width, note: there is a maximum at
0 = 0
sin(a)
па
Intensity:
I(0) = ,,
a =
-sin(0)
m
a
Circular aperture: First minimum: sin 0 = 1.22-
Rayleigh's criterion ( 1 <d ): a =1.22-
d
Double slit experiment with slit separation d and slit width a:
sin a
Intensity: I(0) = I„(cos? B)|
where
B =
-sin 0 , a =
па
-sin O
Grating equation (normal incidence): d sin 0 = m
order in which the grating is being used, d is the line or groove spacing
m
= 0,1, 2,3,... (maxima), where m is the
Transcribed Image Text:3.
Light from an emission line lamp is normally incident on a transmission diffraction grating
with 550 lines per mm.
What is the diffraction angle 0 (in degrees) for a spectral line with a wavelength of
2 = 565.270 nm observed in second order?
а.
b.
What is the minimum resolution, R, for the above spectral line to be just resolved from
another spectral line at 1, = 565.285 nm?
%3D
How many grooves or lines on the grating must be illuminated in order to achieve the
above resolution in second order.
С.
What minimum size, D, grating (550 lines per mm) is needed to achieve the resolution in
part b.) in second order?
d.
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