2. A very narrow slit of width = 2.50µm is illuminated with light of wavelength 1 = 540.0 nm and a diffraction pattern is observed on a screen D=1.25 m from the slit. At the screen, how far from the optical axis, y, , is the second minimum that appears on а. 2' either side of the central maximum? b. At the screen, how far from the optical axis, ymay , is the furthest minimum that appears on either side of the central maximum?
2. A very narrow slit of width = 2.50µm is illuminated with light of wavelength 1 = 540.0 nm and a diffraction pattern is observed on a screen D=1.25 m from the slit. At the screen, how far from the optical axis, y, , is the second minimum that appears on а. 2' either side of the central maximum? b. At the screen, how far from the optical axis, ymay , is the furthest minimum that appears on either side of the central maximum?
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Transcribed Image Text:2.
A very narrow slit of width a = 2.50µm is illuminated with light of wavelength
1 = 540.0 nm and a diffraction pattern is observed on a screen D=1.25 m from the slit.
At the screen, how far from the optical axis, y2 , is the second minimum that appears on
а.
either side of the central maximum?
b.
At the screen, how far from the optical axis, ymax
is the furthest minimum that appears on
either side of the central maximum?
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
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