Download Laser Refraction and Diffraction

General Physics Experiment Handout
Laser Refraction and Diffraction
Purpose
Observe the refraction and diffraction of a laser beam, and understand the functions of
optical components such as single-slit, double-slit, and diffraction grating.
Principles
Based on Snell’s law, the refractive index of a glass plate is determined by the principle
of refraction. In addition, the principles of diffraction and interference support
qualitative and quantitative experiments using single-slit, double-slit, or multiple-slit
(diffraction grating) apparatuses.
A. Snell's law
As shown in Fig. 1, Snell’s law, a formula that is crucial in geometric optics,
describes the relationship between angles of incidence and refraction regarding light
passing through the interface between two media.
Figure 1. Diagram of the angles of incidence and light refraction on a surface
When light is propagated from Medium 1 to Medium 2, some of the light is reflected
and some light is refracted. θi, θr, θt are the angles of incidence, reflection, and
refraction, respectively. n1 and n2 are the refractive indices of Mediums 1 and 2,
respectively. According to Snell’s law, these parameters follow the formulae below.
θi = θ r
n1 sin θi = n2 sin θt
(1)
(2)
We illuminate a glass plate using a laser beam to verify Snell’s law and determine the
refractive index of a given glass.
B. Diffraction and interference
Light, as described in geometrical optics, propagates along a specific straight
line. Shadows form when the propagated light is obstructed by objects. However,
experiments have shown light and dark band results that do not match the descriptions
of geometrical optics. Light bands have been observed in some places that are expected
to be dark.
This phenomenon cannot be explained by geometrical optics principles that
1/5
General Physics Experiment Handout
describe light propagation as traveling along a straight line. Thus, the concept of wave
optics based on “waves” must be introduced for further analyses. One crucial principle
that forms the foundation of wave optics is the Huygens-Fresnel principle proposed by
Christiaan Huygens and Augustin-Jean Fresnel. This principle holds that a wavefront is
composed of numerous small wave sources. These sources produce additional waves at
the position of the wavefront, which leads to subsequent wavefronts that produce more
subsequent wavefronts according to the assumptions of this principle. Various
phenomena of diffraction and interference can be qualitatively and quantitatively
explained using this important principle.
As shown in Fig. 2, if a single slit is illuminated with a plane wave (light), dark
bands are formed when the wave satisfies Formula 3. Wavefronts in the plane wave are
parallel to each other. A ray composed of this type of wave is either highly directional
or possesses a small divergence angle.
a sin θ = mλ , m = intengers
(3)
where a is the width of the slit, θ is the observation angle, and λ is the light wavelength.
When θ is small, a sin θ ≈
ax
z
.
Figure 2. Diagram of single-slit diffraction
Thus, minima appear at specific and regular positions. Minima in an interference
pattern can be determined by
The first minimum x1 = λ z a
The second minimum x2 = 2λ z a
The third minimum x3 = 3λ z a
……
The mth minimum xm = mλ z a , m = integers
The distance between two minima is ∆x = xm − xm −1 = λ z a , and the intensity distribution
sin α 

 α 
of single-slit diffraction can be calculated using I ( x ) = I m 
α=
2
, where
πa
π ax
sin θ ≈
.
λ
λz
As shown in Fig. 3, a double slit is illuminated by a plane wave, where a is the
width of the slits and b is the space between the slits. Assuming that a is extremely
2/5
General Physics Experiment Handout
small, each wavefront of each slit can be considered a new point source that emits light
waves that illuminate the observational plane (plane X-Y). Given these assumptions,
the condition for constructive interference is as follows:
b sin θ = mλ , m = integers
(4)
x
z
Considering sin θ θ
, the distances between the lines of constructive
interference is
∆x = xi − xi −1 =
λz
b
.
Compared to ideal slits, each real slit possesses a certain width. Thus, based on
the Huygens-Fresnel principle, we can speculate that numerous point sources exist at
each slit and produce subsequent waves onto the back of the slit. Secondary point
sources located at the same slit have effects that are similar to single-slit diffraction.
Patterns on the observational plane formed by double-slit diffraction can be
quantitatively described according to the light distribution intensity, that is,
 sin α 
I (θ ) = I m ( cos 2 β ) 

 α 
2
.
Figure 3. Diagram of double-slit diffraction
Figure 4. Pattern of double-slit diffraction (Halliday: Fundamentals of Physics)
As shown in Fig. 5, we extended the slit interference concept and considered a
great amount of slits that were extremely narrow. When multiple-slit apparatus is
illuminated by a ray, the resulting interference can be considered to be produced by
numerous light point sources. Constructive interference caused by numerous light point
sources occurs only at specific angles:
d sin θ = mλ , m = integers
(5)
(this formala is based on the assumption that a considerable distance exists between the
3/5
General Physics Experiment Handout
multiple slit and the observation plane). Diffraction grating, using the principle of
multiple-slit diffraction, is an optical component that is widely adopted in
spectrometers.
Figure 5. Diagram of the path of double-slit diffraction (Halliday: Fundamentals of Physics)
Experimental instruments
1. He-Ne laser source
2. Glass plate
3. Single-slit, double-slit, and diffraction grating
4. Tape measure
Notes
※ The laser can be switched on throughout the experiment.
※ Contact between the lens surface and tools or fingers is strictly forbidden. Do not
look directly at the laser beam, or any reflection of the laser.
Procedures
A. Measurement of the refractive index of a glass plate
1. Use Fig. 1 to calculate the refractive index of a glass plate.
2. Illuminate the glass plate with a laser beam at a predetermined incident angle.
3. Mark the following spots:
☉ The “spot of output” at the output of the laser.
☉ The “spot of incidence” on the glass plate.
☉ The “spot of refraction” on the other side of the glass plate.
☉ Any spot of the reflected beam.
4. Use the marked spots to calculate the angles of incidence, refraction, and
reflection.
5. Let the refractive index of air be na, and use Snell’s law to calculate the
refractive index of the glass plate.
6. Repeat Procedures 1 to 5 for 3 to 5 iterations to calculate the refractive indice
average and errors.
7. Determine the possible refractive index of a glass plate.
B. Slit and grating diffraction
4/5
General Physics Experiment Handout
(The wavelength of the laser used in this experiment was 632.8 nm)
1. The above figure shows the instrument setup. S1 is the position of the single-slit,
double-slit, and diffraction grating; S2 is the observation plane where the
diffraction pattern was observed, and z is the distance between S1 and S2.
2. The angle of incidence should be perpendicular to the optical components (slits
and grating) when using a laser beam to illuminate the slits and grating. In
addition, ensure the laser beam illuminates both slits simultaneously to produce
double-slit diffraction.
3. Place single-slit, double-slit, or diffraction grating at S1.
4. Illuminate the component at S1 using a laser beam. Observe the pattern of
diffraction (or interference) on the observation plane S2, and identify the
position of the maxima and minima at the center of the pattern.
5. Measure the distance  x between bands of the diffraction (or interference)
pattern on the observation plane S2.
6. Measure the distance z between S1 and S2.
7. Use the measurement results to determine the specifications, such as the slit
width and the spacing between slits, for the component at S1.
8. Repeat Procedures 4 to 8 for 3 to 5 iterations to calculate the measurement
average and errors.
9. Switch the component at S1, and repeat Procedures 4 to 8.
※ Remember to limit the laser beam to the range of your laboratory table when
adjusting the laser. Do not direct the beam into other students’ areas. Please protect
your eyes from the laser beam!
Discussion questions
1.
2.
3.
Why is a laser employed instead of other light sources in this experiment? Can a
light bulb be used as the light source?
How does the wavelength of a laser beam affect its interference and diffraction?
Does the angle of incidence of the laser beam affect the interference or
diffraction result on the other side of the slits?
5/5