Diffraction Grating: Laser Illumination & 643 nm Wavelength

In summary, a laser with a wavelength of 643 nm is used to illuminate a diffraction grating with a spacing of 637 lines per mm. The grating is located 11.6 cm in front of a screen. Using the equation wavelength = (s/m)(ym/sqrt(L^2+ym^2)), where s = 1/637 mm, L = 116 mm, and wavelength = 643 x 10^-6 mm, the distance to the first and second maxima (y1 and y2) can be found. However, the answer obtained is incorrect and alternative methods may need to be explored.
  • #1
cyclonefb3
7
0

Homework Statement



A laser is used to illuminate a diffraction grating that has spacing of 637 lines per mm. The grating sits 11.6 cm in front of a screen. Find the distance to the first and second maxima (y1 and y2) for the laser wavelength of 643 nm. Express your answers in mm.

Homework Equations



wavelength = (s/m)(ym/sqrt(L2+ym2))

The Attempt at a Solution



s = 1/637 = .00156 mm
L = 116 mm
wavelength = 643 X 10-6 mm

I tried solving this equation for ym, but the answer I got was wrong. Is there another way to do this problem?
 
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  • #2
Hi cyclonefb3,

What answers did you get?
 
  • #3
I got 116 mm for both.
 
  • #4
cyclonefb3 said:
I got 116 mm for both.

Can you show the details of how you got those two answers (what numbers you used and so forth)? I'm not getting that from your equation.
 

Related to Diffraction Grating: Laser Illumination & 643 nm Wavelength

1. What is a diffraction grating?

A diffraction grating is a device that consists of a large number of equally spaced parallel lines or grooves. These lines act as a diffraction grating that splits and diffracts light into its component wavelengths.

2. How does a diffraction grating work?

A diffraction grating works by using the principle of diffraction, which is the bending of light as it passes through a narrow slit or aperture. When light passes through the parallel lines on the grating, it is diffracted at different angles depending on its wavelength. This results in the separation of the different wavelengths of light.

3. What is the significance of using a laser for illumination in diffraction grating experiments?

Lasers are used for illumination in diffraction grating experiments because they produce a high-intensity, monochromatic (single-wavelength) light source. This makes it easier to observe the diffraction pattern and accurately measure the angles of diffraction.

4. What is the 643 nm wavelength used for in diffraction grating experiments?

The 643 nm wavelength is commonly used in diffraction grating experiments because it falls within the visible spectrum, making it easier to observe and measure. It is also a common wavelength used in red lasers, making it easily accessible for experimentation.

5. What are some real-world applications of diffraction gratings?

Diffraction gratings have a wide range of real-world applications, including in spectroscopy, optical communication, and entertainment (such as in holograms and 3D movies). They are also used in scientific instruments like spectrometers to analyze the composition and properties of materials.

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