The Diffraction Grating -Objective: To measure the wavelength of various lines in the mercury, hydrogen and helium spectra using a diffraction grating. Theory: The diffraction grating is one of the simplest devices for producing spectra (spread-out color contents of a beam of visible light) and measuring wavelengths. There are two types of diffraction gratings: the reflection grating and the transmission grating. A reflection grating consists of a polished metal surface upon which fine, mogul parallel, equally spaced lines are ruled. The incident light is reflected from the grating. The transmission grating consists of lines ruled on glass. The unruled portions act as slits through which light may pass. In this experiment we shall use the transmission type of grating. S X "To 1047 (em) Letd B G Grating Figure 1 - Monochromatic (single-colored) light incident on a transmission diffraction grating Figure 1 shows monochromatic light incident on a transmission grating. Light striking the screen will be in phase and, therefore, produce a point of maximum intensity at point P on the screen provided that the distance BG is an integral multiple of the wavelength of the source. If d is the distance between slits, BG = d sin 0, where 0 is the angle at which the light leaves the diffraction grating. A point of maximum intensity will be formed at P if: 9isood aniturg domi Tag eonil 090.caris a 3 d sin 0 = na works es enwager qu ise . I drawllib sbull Tot Benil griwoflot ord sid amwhere n is an integer. If n= 1, distance CF= 22, distance DE= 31 etc. In other words, the optical path length for each successive ray is 12 greater than the previous ray. This is called the first-order image. If n=2, BG= 21, CF= 42, DE= 62 etc. In other words, the optical path length for each successive ray is 21 greater than the previous ray. The image formed on the screen when this condition exists is called the second-order image.The Diffraction Grating The second-order image will be formed at an angle 0 greater than the angle for the first - order image. Higher-order images will also exist, but each higher order image will be dimmer than the previous one. The first-order image is the brightest and therefore easiest to work with. Images for each order are formed on each side of the grating; in other words, if you look to the left or right of the center of the grating, you should see the same thing. The position of the image on the screen depends on the wavelength of the source. For this reason, the red light will be found at the larger angle because it has a larger wavelength. If the source consists of a number of different wavelengths, one image will be found (see Figure 2) for each wavelength for each value of n. If the source is white light, a continuous spectrum will be formed. RULER 12 Y belength Light Source * GRATING EYE Ja vicaold mumbused to iniog s coube on aidtoFigure 2 - Schematic of laboratory set-up for use of a transmission grating. Procedure: 1. Set up apparatus as shown in Figure 2. Use the 15,000 lines per inch grating. Locate the first-order images for each of the following lines for three different values of x, where x is the distance between the grating and the ruler where you will be taking the wureadings of the line locations.got The Diffraction Grating Mercury - 15,000 lines per inch Y (cm) Avg Calculated (A) X Tan 0 0 Sin 0 Wavelength % difference 5790 (cm) Left Right (cm) (nm) 2 3 (bast) Y (cm) Calculated (A) X Avg Y Tan 0 Sin 0 Wavelength %% difference 5461 (cm) Left Right cm) (nm) 1 IN 3 X Y (cm) (A) Avg Calculated (cm) Left Y Right Tan 0 4047 Sin 0 Wavelength (cm) % difference 1 nm) 2 3 A) Tan & Wavelength 4867 (cin) Left (om) -3The Diffraction Grating Mercury 579.0 nm (Yellow) 546.1 nm Green) X 435.8 nm (Blue) 404.7 nm (Violet) foere Helium - 587.6 nm (Yellow) 438.8 nm (Violet) Hydrogen - 656.3 nm (Red) 486.1 nm (Blue) 2. Calculate the average wavelength for each line and compare your value with the accepted wavelength. Remember, the above wavelengths are in nanometers, where 1 nanometer is 1 x 10-9 m. If the grating is 15,000 lines per inch, then the spacing between each line (d in the equation above) is: 2.54x10 nm 15,000 lines / inch nm / line inch Hat ( no ) (A) which enables you to calculate d. 3. Fill all results in the tables below. 4. If time permits, repeat the experiment with the 25,000 line per inch grating and with second-order images. The procedure is the same as above.The Diffraction Grating Helium - 15,000 lines per inch Calculated Y (cm) Avg X Sin 0 Wavelength %% difference (A) Tan 0 (cm) Left Right (cm) nm 5876 2 3 Avg Calculated a Y (cm (A X Tan 0 Sin 0 Wavelength % difference (cm) Left Right 1388 (cm) (nm) 1 Hydrogen - 15,000 lines per inch A X Y (cm) Avg Calculated Y (cm) Left Right Tan 0 Sin 0 Wavelength % difference 6563 cm) (nm) 1 2 X Y (cm Avg (A) Calculated (cm) Y 4861 Left Right Tan 0 Sin 0 Wavelength (cm) % difference 1 (nm W/ N