405

GUIDE QUESTIONS 1. How does slit width affect the result of the experiment? How about slit-screen separation? Are the experiment results consistent with the theory?

Both the slit width and slit-screen separation affect the result of the experiment in such a way that at constant slit width, an increase in slit-screen distance corresponds to a decrease in wavelength. On the other hand at constant slit-screen separation, an increase in slit width corresponds to a positive reaction with regards to the wave length. Therefore, we can say that slitscreen distance is constant slit width. While slit width is directly proportional to wavelength at constant slit screen separation

2. How is diffraction light different from interference of light? Did you find any differences (or similarities) between the result and light patterns formed in the experiment?

Diffraction is the spreading or bending of light waves when moving past an obstacle. Interference on the other hand is the overlapping of 2 waves at a certain position due to the similarity of their nature. The fringes of light are alternating.

3. Discuss examples and/or application of the phenomenon of diffraction and interference of light. An interference of light can be visible on thin films which is evident in the combination of oil and water. For diffraction, the most common application is the x-ray; the figures we see are fringes of light. Another one is the closely spaced tracks on a compact disk which act like as a diffraction grating to form the rainbow pattern we see when looking at the disk.

4. Enumerate and discuss possible sources of error in the experiment.  Limitations of the sense of sight while determining Ym.  The laser does not completely cover the slit  The light coming from the window is also a factor because it still serves as a light source

PROBLEMS 1. Monochromatic light is incident upon a slit of width 0.55mm. a diffraction pattern is formed on a screen 1.50m away. If the distance from the central maximum to the first minimum is measured to be 1.25mm, what is the wavelength of the light. ( )( ) ( )( )

2. What frequency of light produces a diffraction pattern on a screen such that the distance between the first minimum and the third is approximately 4mm? the slit-to-screen distance is 1.00m while slit width is0.80mm. ( )( ) ( )( )

⁄

3. In the problem 2 above, what is the angle of the second minimum?

EXPERIMENT 405: DIFFRACTION Name Program/Year Subject/Section

Group No. Seat No. Date

Pallera, Alexis Romeo C. CE- 2 PHY104L/B1

DATA and OBSERVATIONS λaccepted = 660 nm to 680 nm (λ average = 670 nm) TABLE 1. SINGLE SLIT DIFFRACTION a = 0.16 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.16 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.16 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.08 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ

x = 90 cm ym 0.4 cm 0.8 cm 1.1 cm -0.3 cm -0.8 cm -1.1 cm

Calculated λ 711.11 nm 711.11 nm 651.85 nm 533.33 nm 711.11 nm 651.85 nm 661.75 nm x = 75 cm

ym 0.3 cm 0.6 cm 0.9 cm -0.3 cm -0.5 cm -0.8 cm

Calculated λ 640 nm 640 nm 640 nm 640 nm 5.33.33 nm 568.88 nm 640.37 nm x = 60 cm

ym 0.3 cm 0.5 cm 0.7 cm -0.2 cm -0.4 cm -0.6 cm

Calculated λ 808 nm 666.67 nm 622.22 nm 533.33 nm 533.33 nm 533.33 nm 614.81 nm x = 90 cm

ym 0.7 cm 1.4 cm 2.1 cm -0.5 cm -1.2 cm -1.9 cm

Calculated λ 622.22 nm 622.22 nm 622.22 nm 444.44 nm 533.33 nm 562.96 nm 567.90 nm

03 303 11/15/08

EXPERIMENT 405: DIFFRACTION Name Program/Year Subject/Section

Group No. Seat No. Date

Pallera, Alexis Romeo C. CE- 2 PHY104L/B1

DATA and OBSERVATIONS

TABLE 1. SINGLE SLIT DIFFRACTION (CONTINUED) a = 0.08 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.80 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.04 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.04 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ

x = 75 cm ym 0.6 cm 1.1 cm 1.7 cm -0.6 cm -1.1 cm -1.6 cm

Calculated λ 640 nm 586.67 nm 604.44 nm 640 nm 586.67 nm 568.89 nm 604.45 nm x = 60 cm

ym 0.5 cm 0.9 cm 1.3 cm -0.4 cm -0.9 cm -1.3 cm

Calculated λ 666.67 nm 600 nm 577.78 nm 533.33 nm 600 nm 577.78 nm 592.59 nm x = 90 cm

ym 1.3 cm 2.5 cm 3.7 cm -1.2 cm -2.4 cm -3.6 cm

Calculated λ 577.78 nm 555.55 nm 548.15 nm 533.33 nm 533.33 nm 533.33 nm 546.91 nm x = 75 cm

ym 1 cm 2.1 cm 3.1 cm -1 cm -2 cm -3 cm

Calculated λ 533.33 nm 560 nm 551.11 nm 533.33 nm 533.33 nm 533.33 nm 540.74 nm

03 303 11/15/08

EXPERIMENT 405: DIFFRACTION Name Program/Year Subject/Section

Group No. Seat No. Date

Pallera, Alexis Romeo C. CE- 2 PHY104L/B1

DATA and OBSERVATIONS

TABLE 1. SINGLE SLIT DIFFRACTION(CONTINUED) a = 0.04 mm m 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ

x = 60 cm ym 0.8 cm 1.9 cm 2.9 cm -0.8 cm -19 cm -2.9 cm

Calculated λ 533.33 nm 633.33 nm 644.44 nm 533.33 nm 633.33 nm 644.44 nm 603.7 nm

TABLE 2. TWO SLIT INTERFERENCE a = 0.08 mm / d = 0.50 mm m 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.80 mm / d = 0.50mm m 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ

x = 90 cm ym 0.00 cm 0.1 cm 0.16 cm 0.22 cm -0.09 cm -0.17 cm -0.22 cm

Calculated λ 0 nm 555.56 nm 444.44 nm 407.41 nm 500 nm 472.22 nm 407.41 nm 398.15 nm x = 75 cm

ym 0.00 cm 0.1 cm 0.2 cm 0.3 cm -0.1 cm -0.2 cm -0.3 cm

Calculated λ 0 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 571.43 nm

03 303 11/15/08

EXPERIMENT 405: DIFFRACTION Name Program/Year Subject/Section

Group No. Seat No. Date

Pallera, Alexis Romeo C. CE- 2 PHY104L/B1

a = 0.08 mm / d = 0.50 mm M 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.08 mm / d = 0.25 mm m 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.08 mm / d = 0.25 mm M 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.08 mm / d = 0.25 mm m 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ

x = 60 cm ym 0.00 cm 0.08 cm 0.15 cm 0.24 cm -0.09 cm -0.17 cm -0.25 cm

Calculated λ 0 nm 666.67 nm 625 nm 666.67 nm 750 nm 708.33 nm 694.44 nm 587.30 nm x = 90 cm

ym 0.00 cm 0.2 cm 0.4 cm 0.6 cm -0.2 cm -0.4 cm -0.6 cm

Calculated λ 0 nm 555.55 nm 555.55 nm 648.15 nm 555.55 nm 694.44 nm 740.74 nm 535.71 nm x = 75 cm

ym 0.00 cm 0.2 cm 0.4 cm 0.6 cm -0.2 cm -0.4 cm -0.6 cm

Calculated λ 0 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 571.43 nm x = 60 cm

ym 0.00 cm 0.1 cm 0.3 cm 0.5 cm -0.1 cm -0.3 cm -0.5 cm

Calculated λ 0 nm 416.67 nm 625 nm 694.44 nm 416.67 nm 625 nm 694.44 nm 505.51 nm

03 303 11/15/08

EXPERIMENT 405: DIFFRACTION Name Program/Year Subject/Section

Group No. Seat No. Date

Pallera, Alexis Romeo C. CE- 2 PHY104L/B1

TABLE 2. TWO SLIT INTERFERENCE (CONTINUED) a = 0.04 mm / d = 0.50 mm m 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.04 mm / d = 0.50 mm m 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ a = 0.04 mm / d = 0.50 mm m 0 1 2 3 -1 -2 -3 AVERAGE CALCULATED λ

x = 90 cm ym 0.00 cm 0.1 cm 0.2 cm 0.4 cm -0.1 cm -0.2 cm -0.4 cm

Calculated λ 0 nm 555.56 nm 555.56 nm 740.74 nm 555.56 nm 555.56 nm 740.74 nm 529.10 nm x = 75 cm

ym 0.00 cm 0.1 cm 0.2 cm 0.3 cm -0.1 cm -0.2 cm -0.3 cm

Calculated λ 0 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 666.67 nm 571.43 nm x = 75 cm

ym 0.00 cm 0.08 cm 0.15 cm 0.2 cm -0.09 cm -0.15 cm -0.2 cm

Calculated λ 0 nm 666.67 nm 625 nm 555.56 nm 750 nm 625 nm 555.56 nm 539.68 nm

03 303 11/15/08

SAMPLE COMPUTATION

Table 1. (single slit diffraction)

(

)(

)

(

)

Table 2. (two slit interference)

(

)( (

) )

ANALYSIS Our fifth experiment is all about Diffraction of Light Waves. For this experiment our main objective is to explore the phenomenon of diffraction of light and to compare single slit diffraction and multiple slits interference. To start our experiment, we first investigate the single slit diffraction. In order for us to investigate the diffraction occurring in a single slit disk, we try to change either the slit-screen difference (x) or slit width (a) leaving or setting the other variable as constant. From here, we can get the value for wave length (λ) and eventually analyze its relationship to the slit-screen difference (x) and the Slit width (a). Based on the results of our experiment, I observed that for every increase in the slit-screen distance (x) corresponds to a decrease in the wave length (λ). On the other hand, I observed that at constant slit-screen separation, an increase in slit width (a) corresponds to an increase in value with regards to the wave length (λ). Based on the results of our observations, we can conclude that the results are consistent with the theory which gives the equation,

( ) ( )

where a is the slit width and x is the slit-screen

separation. Since we’ve used a slit disk which has only a single slit, waves are 180° and therefore out of phase resulting to a destructive interface. Destructive interface occurs when a crest of one wave overlaps through another wave resulting to a decrease in amplitude and formation of a dark region known as the central minimum. For the second part of the experiment, the procedures are the same as the first part however the only difference between the two parts were the instrument used; in this experiment we used a double slit disk instead of a single slit disk. Based on the results of our experiment, the observation on the first part is almost the same as the second part. Since we’ve used double-slit disk, waves were in phase resulting to a constructive interference which occurs when crest of the two waves overlap resulting to an increase in amplitude and formation of bright region known as the central maximum. As a whole, single and double slit disk differ on their interference but the relationship regarding slit width, wave length and slit-screen separation are all the same. Diffraction depends only on the ratio of wave length to the size of the diffracting object.

CONCLUSION I therefore conclude the Diffraction refers to various phenomena associated with wave propagation such as bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. Even though Diffraction always occurs, its affects generally most noticeable for waves were the wavelength is on order of the diffracting objects. The complex patterns in the intensity of a diffracted wave are for result of interference between different parts of a wave that traveled to the observer by different paths. The angular spacing of the features in the diffraction angle is inversely proportional to the dimensions of the objects causing the diffraction. The diffraction angles are invariant under scaling; they depend only on the ratio of the wavelength to the size of the diffracting object. The effects of diffraction can be easily seen in everyday life. The closed space tracks on a CD act as a diffracting grating to form a rainbow pattern we seen when looking at the disk. Diffraction in the atmosphere by small particles in it can cause a bright ring to be visible around a bright light source like the sun or the moon. Diffraction can also be a concern in some technical applications; it sets a Fundamental limit to the resolution of camera, telescope or microscope. Interference is the overlapping of two waves. It is a phenomenon which occurs when two waves of the same nature from different sources meet at the same place. Constructive interference when ting amplitude is greater than the amplitude of the two waves that results to the formation of bright region know as the central maximum. On the other hand, Destructive interference occurs when the crest of one wave overlaps the trough of another wave resulting to a decrease in amplitude and the formation of dark region know as the central minimum.