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Use your diffraction grating as follows to measure the wavelengths of the red and green passed by your filters. Put a line (or point) source right next to a wall or door. Make a mark on the wall about a foot to the side of the source. Look at the source through the grating, holding the filter over your grating (or put the filter over the source-but don't melt it!) Move closer and farther from the source until the color of interest appears to be superposed with your mark on the wall. Measure the appropriate distances and calculate \(\lambda\). Thus calibrate the wavelengths transmitted by your red, green, and purple filters. Memorize the results. (Then you can use your filters and the grating to find the wavelengths of other colors when you wish to, without repeating the geometric measurement of this experiment.)

Short Answer

Expert verified
Set up the experiment, view through the grating, align and measure distances, calculate wavelength, then memorize the results.

Step by step solution

01

Set up the Experiment

Position the light source just beside a wall or door. Make a noticeable mark on the wall, approximately one foot to the side of the source. This mark will help you in aligning the visible diffraction pattern.
02

View Through the Diffraction Grating

Place the diffraction grating between your eye and the light source. Hold the color filter (red or green) either over the grating or over the light source. Ensure the filter is not too close to the source to prevent melting.
03

Align the Diffraction Pattern

Move back and forth until the colored diffraction pattern aligns precisely with the mark on the wall that was made earlier. The position where alignment occurs is important for measurement.
04

Measure the Distances

Measure the distance from the light source to the diffraction grating (d). Also, measure the distance from the grating to the wall (x). These measurements are crucial for calculating the wavelength.
05

Calculate Wavelength

Use the diffraction angle equation \[ \lambda = \frac{d \cdot x}{L} \], where \( \lambda \) is the wavelength, \( d \) is the distance to the mark, \( x \) is the distance to the wall, and \( L \) is the distance from the light source to the grating.
06

Memorize the Wavelengths

After calculating the wavelengths for red and green filters, memorize these results. This allows you to use the filters for identifying other wavelengths without recalibrating.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Wavelength Measurement
Measuring the wavelength of light is a fascinating process that involves understanding how light behaves as a wave. In the given experiment, a diffraction grating is used to disperse the light into its constituent colors. This helps in identifying and measuring specific wavelengths.

The key to measuring wavelength lies in the equation \[ \lambda = \frac{d \cdot x}{L} \],where:
  • \( \lambda \) is the wavelength.
  • \( d \) is the distance from the diffraction grating to the wall.
  • \( x \) is the horizontal distance along the wall, aligning the diffraction pattern.
  • \( L \) is the distance from the light source to the diffraction grating.

To accurately measure wavelength, align the diffraction pattern (that is displaced by the angle formed with the source and your mark) and take precise measurements of these distances. With these values, you can calculate the wavelength for red, green, and any other color filters used. This method provides a practical and rewarding way to understand the principles of light and its multi-color spectrum.
Color Filters
Color filters play an essential role in optical experiments, especially those involving diffraction gratings. These filters allow only certain colors (or wavelengths) of light to pass through, blocking the others. In the experiment, filters for red and green are used to isolate these specific light wavelengths.

Using color filters, you can select which color you want to measure by filtering out all others. This helps in making a precise measurement of the wavelength corresponding to the particular color.

When a red filter is placed over a light source or a diffraction grating, it only lets through the red part of the spectrum. The same goes for the green filter with the green portion of the spectrum. This selective transmission allows for clear and specific wavelength measurement without interference from other colors.

By understanding how color filters work, you can effectively conduct experiments related to light and optics, identifying distinct wavelengths for different colors.
Optical Experiment
Conducting optical experiments with diffraction gratings and color filters is an engaging way to delve into the world of light physics. This type of experiment helps students grasp core concepts by observing real-world applications.

In the exercise, you use a line or point source beside a wall and observe the light through a diffraction grating placed at a certain distance. By moving back or forth, the alignment of the visible diffraction pattern with a pre-marked point on the wall becomes crucial.

Observing this alignment allows for precise distance measurements needed for wavelength calculations. This type of setup underscores essential scientific practices like hypothesis testing, experimentation, and data collection.

These optical experiments enhance understanding not just of wavelengths but also of how light interacts with different materials. They demonstrate the principles of optics and prepare students for more advanced studies in physics or engineering.

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Most popular questions from this chapter

A point object is 2 meters from a positive lens of power 1 diopter. Where is the image? (The object is on the lens axis.)

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A double slit of slit separation \(0.5 \mathrm{~mm}\) is illuminated by a parallel beam from a helium-neon laser that emits monochromatic light of wavelength \(6328 \AA\). Five meters beyond the slits is a screen. What is the separation of the interference fringes on the screen?

Show that a plane wave normally incident on one face of a wedge-shaped prism of angle \(A\) is deviated by an amout \(\theta_{\text {dev }}\), where $$ n \sin A=\sin \left(A+\theta_{\text {dev }}\right) \text { . } $$

Burn a piece of toilet paper and look at it through your diffraction grating (held, as always, close in front of one eye). Notice the beautifully clear "first-order flame." This shows that the soft yellow light is almost monochromatic, with very little "white light" color spectrum due to hot carbon. The yellow that you see is the by now familiar (we hope) sodium doublet of wavelengths 5890 and \(5896 \AA\). Now that you recognize "sodium yellow," light an ordinary paper match and look at it with your grating. Most of the light is "hot carbon yellow," which is not really yellow but a complete "white" color spectrum. But look closely! In the yellow part of the hot carbon spectrum, down low next to the cardboard, where the flame is "blue" looking-below the blindingly bright hot carbon spectrum-do you see a crisp, clear little monochromatic match flame? If you don't, try again! Now burn other things and look. You may well conclude that everything is made of salt or is at least contaminated by it.

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