Assume that your eye acts as a diffraction limited telescope with a round primary aperture of diameter D= 4.50 mm . Two lights are arranged to be perpendicular to your line of sight with a separation of s = 20.0cm (assuming Rayleigh's criterion): If the lights emit at 1, 1. a. 630 nm what is the furthest distance that we will see them as two separate lights, d,? A b. If the lights emit at 1R :440 nm what is the furthest distance that we will see them as two separate lights, d;? B
Assume that your eye acts as a diffraction limited telescope with a round primary aperture of diameter D= 4.50 mm . Two lights are arranged to be perpendicular to your line of sight with a separation of s = 20.0cm (assuming Rayleigh's criterion): If the lights emit at 1, 1. a. 630 nm what is the furthest distance that we will see them as two separate lights, d,? A b. If the lights emit at 1R :440 nm what is the furthest distance that we will see them as two separate lights, d;? B
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Transcribed Image Text:Assume that your eye acts as a diffraction limited telescope with a round primary
aperture of diameter D = 4.50 mm . Two lights are arranged to be perpendicular to your line
1.
20.0cm (assuming Rayleigh's criterion):
of sight with a separation of s =
If the lights emit at 1, = 630 nm what is the furthest distance that we will see them as two
а.
separate lights, d?
b.
If the lights emit at 1, = 440 nm what is the furthest distance that we will see them as two
separate lights, 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
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