SSM WWW The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See Fig. 36-8 b .) (a) Show that the intensity drops to one-half the maximum value when sin 2 α = α 2 / 2. (b) Verify that α = 1.39 rad (about 80°) is a solution to the transcendental equation of (a) (c) Show that the FWHM is ∆θ = 2 sin –1 (0.443λ/ a ), where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00λ, (e) 5.00λ, and (f) 10.0λ.
SSM WWW The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See Fig. 36-8 b .) (a) Show that the intensity drops to one-half the maximum value when sin 2 α = α 2 / 2. (b) Verify that α = 1.39 rad (about 80°) is a solution to the transcendental equation of (a) (c) Show that the FWHM is ∆θ = 2 sin –1 (0.443λ/ a ), where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00λ, (e) 5.00λ, and (f) 10.0λ.
SSM WWW The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See Fig. 36-8b.) (a) Show that the intensity drops to one-half the maximum value when sin2 α = α2/2. (b) Verify that α = 1.39 rad (about 80°) is a solution to the transcendental equation of (a) (c) Show that the FWHM is ∆θ = 2 sin–1(0.443λ/a), where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00λ, (e) 5.00λ, and (f) 10.0λ.
Statistical thermodynamics. The number of imaginary replicas of a system of N particlesa) cannot be greater than Avogadro's numberb) must always be greater than Avogadro's number.c) has no relation to Avogadro's number.
Lab-Based Section
Use the following information to answer the lab based scenario.
A student performed an experiment in an attempt to determine the index of refraction of glass.
The student used a laser and a protractor to measure a variety of angles of incidence and
refraction through a semi-circular glass prism. The design of the experiment and the student's
results are shown below.
Angle of
Incidence (°)
Angle of
Refraction (º)
20
11
30
19
40
26
50
31
60
36
70
38
2a) By hand (i.e., without using computer software), create a linear graph on graph paper
using the student's data. Note: You will have to manipulate the data in order to achieve a
linear function.
2b) Graphically determine the index of refraction of the semi-circular glass prism, rounding your
answer to the nearest hundredth.
Use the following information to answer the next two questions.
A laser is directed at a prism made of zircon (n = 1.92) at an incident angle of 35.0°, as shown in
the diagram.
3a) Determine the critical angle of zircon.
35.0°
70°
55
55°
3b) Determine the angle of refraction when the laser beam leaves the prism.
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