3-The Prism Spectrometer Autosaved

Spectrometer 2010

‐ 1 ‐ ARWA TALAL KUTBEE

Prism Spectrometer

ARWA TALAL KUTBEE

Spectrometer 2010


Table of Contents

Section Page Back ground ........................................................................................................ 3 Basic Experiments Experiment 1: Prism spectrometer ........................................................... 6

Spectrometer 2010


Back ground

reflection and refraction :

the law of reflection states that for a light ray travelling in air and incident on a smooth surface , the angle of reflection equals the angle of incidence :

light crossing a boundary as it travels from medium 1 (with light speed ) to medium 2 (with light speed ) is refracted or bent . the angle of refraction is

defined by the relationship :

From this equation we can infer that when light moves from a material in which its speed is high to a material in which its speed is lower ,the ray is bent toward the normal and vice versa.

index of refraction : the index of refraction is a property of a medium and defined by n

where c is the speed of light in vacuum and v is the speed of light in the medium .In

general ,n varies with wavelength and is given by n

where λ is the vacuum wavelength and λ is the wavelength in the medium .note that as light travels from one medium to another it s frequency remains the same .

snell's law of refraction states that:

sinsin

Where and are the indices of refraction for the two media.The incident ray ,the reflected ray ,the refracted ray and the normal to the surface all lie in the same plane.

Dispersion: Dispersion is the phenomenon which gives you the separation of colors in a prism.

For a given material, the index of refraction varies with the wavelength of the light passing through the material. Fig.1

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The relation between the refractive index and wavelength of light for a particular transparent material is given by Cauchy's equation :

n λ ABλ

where A and B are material-dependent constants. Note that the larger the value of B, the more dispersive the medium.

A table of coefficients for common optical materials is shown below:

Glass A B (μm2)

BK7 1.5170 0.00422

dense flint 1.5961 0.00880

hard crown 1.5043 0.00455

Table.1

Because is a function of wavelength, light of different wavelengths is bent at different angles when incident on a refracting material. the index of refraction generally decreases with increasing wavelength (for visible light). This means that violet light bends more than red light does when passing into a refracting material. white light can be separated by a dispersive medium like a prism. Even more effective separation can be achieved with a diffraction grating.

the separation of colors by a prism we see the continuous range of spectral colors (the visible spectrum). A spectral color is composed of a single wavelength and can be correlated with wavelength as shown in the chart below

This progression from right to left is from long wavelength to short wavelength, and from low frequency to high frequency light.

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Prism :

A refracting prism is a convenient geometry to illustrate dispersion. Prisms are typically characterized by their angle of minimum deviation .

When a ray of single wavelength light incident on a prism from the left it emerges refracted from its original direction of travel by an angle δ , called the angle of deviation Figure.2

The minimum deviation angle δ can be achieved by adjusting the incident ray

perpendicular to one of the prism's sides which leads that the ray passing through the prism

to be parallel to the bottom of the prism.

And the incident angle =the refracting angle

Using the geometry in the figure, we find that

θ

Where is the apex angle of the prism .

θ θ α2

δ2

δ2

From snell's law of refraction, with n 1 because. Figure.3

medium 1 is air

sin θ n sin θ

sinδ2

n sin2

nsin

δ2

sin 2

Hence .knowing the apex angle of the prism and measuring the angle of minimum deviation we can calculate the index of refraction of the prism material.

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Experiment 1: Prism spectrometer

Spectrometer: A spectrometer is an optical instrument for producing and analyzing spectra.

The importance of the spectrometer as a scientific instrument is based on a simple but crucial fact. Light is emitted or absorbed when an electron changes its orbit within an individual atom. Because of this, the spectrometer is a powerful tool for investigating the structure of atoms. It's also a powerful tool for determining which atoms are present in a substance. Chemists use it to determine the constituents of molecules, and astronomers use it to determine the constituents of stars that are millions of light years away. a spectrometer consists of three basic components As shown in Figure 4; a collimator, a diffracting element(prism or diffraction grating) , and a telescope. The light to be analyzed enters the collimator through a narrow slit positioned at the focal point of the collimator lens. The light leaving the collimator is therefore a thin, parallel beam, which ensures that all the light from the slit strikes the diffracting element at the same angle of incidence. This is necessary if a sharp image is to be formed. The diffracting element bends the beam of light. If the beam is composed of many different colors, each color is diffracted to a different angle. The telescope can be rotated to collect the diffracted light at very precisely measured angles. With the telescope focused at infinity and positioned at an angle to collect the light of a particular color, a precise image of the collimator slit can be seen.

Figure 4 Spectrometer diagram

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Equipment –Spectrometer :which consists of a)Collimator and Telescope collimator is fitted with a 6 mm long slit of adjustable width. The telescope has an eyepiece with a glass, cross-hair. b)Rotating Bases The telescope and the spectrometer table are mounted on independently rotating bases. Vernier scales provide measurements of the relative positions of these bases to within one minute of arc. The rotation of each base is controlled with a lock-screw and fine adjust knob. With the lock-screw released, the base is easily rotated by hand. With the lock-screw tight, the fine adjust knob can be used for more precise positioning. c)Spectrometer Table The spectrometer table is fixed to its rotating base with a thumbscrew, so table height is adjustable. Three leveling screws on the underside of the table are used to adjust the optical alignment. Thumbscrews are used to attach the prism clamp and the grating mount to the table, and reference lines are etched in the table for easy alignment. –Equilateral glass prism. –Spectrum tube power supply. –Spectrum tubes such as Mercury, Helium, Cadmium, etc. –magnifier.

Figure 5 Spectrometer with working parts. Not shown is the vernier window on

the opposite side

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OBJECTIVE 1) Learn the theory of the prism spectrometer, and explain the functions of its various components. 2) Measure the apex angle of the prism . 2) Observe the spectrum of the discharge lamp and record the angle of minimum deviation for the spectral lines. 3) Determine the index of refraction of a glass prism for various colors and to examine how the index of refraction of the material of a prism depends on the wavelength of light. 4) Calculate the dispersive power for each color in the spectrum using the Cauchy equation. 5)determine the Cauchy constants from the plot .and to determine what type of glass constitutes the prism. 6) Calculate the dispersive power of the prism . PROCEDURE 1. Turn on the mercury light. It takes a while to warm up.

To save time and frustration, the spectrometers are adjusted through Step 10. Take the following steps only if instructed to do so by your TA.

Focus Adjustment

2. With no prism on the prism table, focus the telescope at infinity (something at one end of the room or through the window, not through the collimator). You may have to loosen the telescope rotation lock screw to freely move the telescope.

3. While looking through the telescope, slide the eyepiece in and out until the cross hairs come into sharp focus. Do not use the focusing knob to do this. There is a locking adjustment around the eyepiece that you can loosen. When you tighten it up again, make sure the cross hairs are aligned so that one is totally horizontal and the other is vertical. (If it’s rotated a little, it’s hard to align the spectral lines.)

4. If necessary, repeat steps 2 & 3 until the distant object and the cross hairs can be put in sharp focus at the same time.

5. Check to see that the collimator slit is partially open. Adjust, if necessary. 6. View the collimator slit through the telescope. Focus the collimator (not the

telescope) until the slit comes into sharp focus. 7. Lock the telescope rotation lock screw. Use the telescope rotation fine adjustment

to align the vertical cross hair with the fixed edge of the slit. (The fine adjust does not work unless the rotation lock screw is set.)

Spectrometer 2010


Zeroing the Reference Angle

8. Loosen the table base lock screw and rotate the table so that the right window vernier reads about 0°. Retighten the lock screw.

9. Using the magnifier and the table base fine adjust, set the vernier to read 0° 0'. This is

your reference angle.( Notice that there are two windows in which you can read an angle. We want to rotate the table until one of the windows has 0 (zero), we should try to use set it so that this window is to the left of the telescope (as we are looking over the barrel toward the lamp) because this will make reading our angle easiest. Setting this to zero means that the vernier reading for a particular spectral line is directly the angle of minimum deviation. Do not move the table after you have set this angle.

Prism Mounting

10. Mount the prism at the center of the prism table. If necessary, loosen the (long) table lock screw which fastens the prism table to the base and adjust the height so that light from the collimator is striking the prism, then lightly tighten the screw. Recall that the prism orientation for the minimum deviation is where one of the sides is roughly perpendicular to the incident light beam(the refracted light is parallel to one of the sides of the prism), as in Fig. 3. The frosted side of the prism should be to the right as you’re facing the light source.

Measuring the Apex angle 11.Place the prism on the turntable with its frosted side hard against the lamp and rotate the table until the beam from the collimator is roughly bisected by the apex of the prism as in figure 6.The beam will be reflected off both sides of the prism (each acting like a plane mirror) so two images of the slit can be observed, one on each side of the prism. The angle between the two telescope positions is twice the angle of the prism.

Minimum Deviation Adjustment

12. Set up the spectrometer to view light from the mercury lamp. (See Fig. 7) Based on Fig. 3, estimate the direction the dispersed light from the collimator will exit the prism. With your bare eye, look at the prism along this direction to find the image of the collimator's slit. You should see a series of brightly-colored lines.

Note: measurements should always be made with the cross hairs aligned on the fixed edge of the collimator slit. This enables you to adjust the slit's

2

Figure.7

Figure.6

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width for optimal line visibility at any time during data collection. This way, your angle measurement is independent of the width of the slit.

13. If the prism is in exactly the right orientation to provide the angle of minimum deviation, the series of colored lines move to the right as a whole, whether you rotate the table clockwise or counterclockwise. rotate the table until you are satisfied that the orientation is where the lines bounce, or change direction.

14. Now view the lines through the telescope. a. Rotate the prism back and forth slightly to fine-tune the exact orientation that

puts the lines at their extreme position (the telescope's cross hairs make a convenient reference mark).

b. Since the position of the prism for minimum deviation is a slowly varying function of the wavelength, it is not necessary to reset the minimum deviation for each line (color). Once the prism is set, this orientation should not be changed for the duration of the experiment.

c. Lightly tighten the prism holder.

Measure

15. Measure for line in the mercury spectrum: a. Loosen the telescope rotation lock screw and rotate the telescope so that its

cross hairs are near the fixed-edge side of the slit's image. b. Lightly tighten the telescope rotation lock screw. c. Use the telescope fine adjust knob to carefully align the cross hairs and the

fixed-edge side of the slit's image. d. Find the value of for this color using the vernier scale.

i. Identify the color from (fig.8) and record the wavelength of the line from (Table 2).

ii. Record the two numbers from the spectrometer that indicate this angle, the nearest, lowest half-degree and the minute.

Light

Source Line Color Wavelength

(Å) Mercury Red 6907

Yellow 5790 Yellow 5770 Green 5461 Blue-Green 4916 Blue 4358 Violet 4078 Violet 4047

Figure.8

table.2

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Reading the Angle

The angle between the moveable telescope and the fixed collimator is determined using the vernier scale as in (Fig. 9) The bottom degree plate is graduated in units of 0.5° or 30' (30 arc minutes). The top set of numbers, or the vernier scale, provides a further resolution of 1' and has a range of 30'. Reading this type of vernier is the same in principle as the one with the calipers . Follow the procedure below:

Figure 9 The half degree-minute vernier on the spectrometer.

A. Find the Zero. Locate where the zero mark of the vernier scale aligns with the degree plate.

B. Record the degrees to the nearest, lowest 0.5°. When the zero of the top scale is between two lines on the degree plate, use the smaller value. (In Fig. 9), the zero is between the lines 155° and 155° 30'. 155° is the smaller of the two, so you record the degrees as 155.

C. Record the minutes. Use the magnifying glass to determine the line on the vernier scale that aligns most closely with any line on the degree plate. (In Fig. 9), this is 15', so you write down 15 as the minutes.

D. Add this value to the reading recorded above to get the correct measurement to within 1 minute of arc: that is, 155 ° + 15' = 155 °15'.

Hints:

Opening up the slit allows more light to come through, increasing the intensity and allowing you to better see the dimmer lines. However, some of the lines are so close to each other that a wider slit washes out the distinction. In particular, the two yellow lines of mercury need a very narrow slit in order to distinguish between the two.

Also, repositioning the lamp can increase the brightness.

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You can also use the blackout cloth to shield the prism from unwanted light.

ANALYSIS

1.Based on your use of the spectrometer to measure δ , Determine the index of refraction of a glass prism for various colors using the equation :

n

Plot the diagram that indicates the relation between

on the x axis vs. n on the y axis

From the plot :

a. Identify the obtained plot.

b. examine how the index of refraction of the material of a prism depends on the wavelength of light.and by what equation are they related .

c. by assuming the obtained plot is approximately a straight line ,find the value of the

Cauchy constants. n λ A B

where A,B are Cauchy constants slope=B V.I=A

d. Determine what type of glass constitutes the prism from the obtained values of the Cauchy constants in (table.1) e. calculate the error. 2. Calculate the dispersive power for each color (d) using Cauchy equation

Where: D B

The obtained table should look like the following: color δ

(degree) n λ (nm) 1

λ

λ D

3.Calculate the dispersive power of the prism (p)

a. Find the intermediate wave length using the relation :

λ:The intermediate wave length , λ : The shortest wave length =λ , λ : The longest wave length=λ .

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b. Draw a graph that indicates the relation between : λ on the X-AXIS vs. n on the Y-AXIS.

c. Locate the position of λ on the digram and its corresponding n

d. Use the relation to calculate the dispersive power of the prism p

n is the Refractive index of the shortest wave length, (n is the Refractive index of the longest wave length ,(n is the Refractive index of the intermediate wave length and p is the Dispersive power of the prism.