Diffraction Grating problem

In summary, the conversation discusses the calculation of the width of narrow vertical slits in a diffraction grating light pattern. The data provided includes the distance to the screen, wavelength of light, and distance between tick marks on the intensity figure. Using the formula for maxima, the angle theta is found to be 0.33095 degrees. However, when plugging into the formula for maxima, a width of 72.7 micrometers is calculated, which is found to be incorrect. The conversation ends with a question about possible errors in the calculation.
  • #1
mrbling
14
0
Question: A set of narrow vertical slits is located a distance D from a screen. The slits are equally spaced and have the same width. The intensity pattern in the figure is observed when light from a laser passes through the slits, illuminating them uniformly. The screen is perpendicular to the direction of the light.


Calculate the width of the slits, in micrometers.

You are given the following data: Distance to the screen = 2.77 meters; Wavelength of light = 0.420 micrometers; Distance between tick marks on the intensity figure = 1.60 cm (The figure has the generic diffraction grating light pattern, with tick marks occurring between each maxima)

Maxima occur at sin theta = m lambda / d (where m is the order, lambda is the wavelength of light, and d is the distance between slits)

first.. I find out what theta is.. i can find this by
tan theta = (.016m)/(2.77m)
tan theta = .0057761
theta = .33095 degrees

plugging into the maxima formula,
sin theta = m lambda / d
sin (.33095) = 1 (.420x10^-6) / d
d = 7.27x10^-5m = 72.7 micrometers

72.7 micrometers is incorrect. Anyone know where I went wrong?

Thanks.
 
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  • #2
Any thoughts on this problem?

It seems so straight forward that I can't see where I may have gone wrong..

Thanks..
 
  • #3


It looks like you made a small error in your calculation for theta. The correct value for theta is actually 0.33095 radians, not degrees. So the correct calculation would be:

sin(0.33095) = 1(0.420x10^-6) / d
d = 7.27x10^-5 m = 72.7 micrometers

Therefore, the width of the slits would be approximately 72.7 micrometers. It is always important to double check your units and make sure you are using the correct values for your calculations. In this case, converting from radians to degrees caused the error in your result.
 

What is a diffraction grating?

A diffraction grating is an optical component that is used to separate and analyze light into its component wavelengths. It consists of a large number of parallel, equally spaced lines or slits that are etched onto a flat surface. When light passes through the grating, it is diffracted into different directions, creating a spectrum of colors.

What is the purpose of a diffraction grating?

The main purpose of a diffraction grating is to separate and analyze different wavelengths of light. This is useful in many applications, such as spectroscopy, where the grating can be used to identify the chemical composition of a substance based on its unique spectral signature.

How does a diffraction grating work?

When light passes through a diffraction grating, it encounters the parallel lines or slits on the surface. Each slit acts as a point source, emitting light in all directions. The light waves from each slit interfere with each other, creating a pattern of bright and dark spots. The spacing between the lines on the grating determines the angle at which the different wavelengths of light will be diffracted, resulting in a spectrum of colors.

What factors affect the diffraction of light by a grating?

The main factors that affect the diffraction of light by a grating are the spacing between the lines, the angle of incidence of the light, and the wavelength of the light. The spacing between the lines determines the angle at which the light is diffracted, while the angle of incidence and the wavelength of the light affect the intensity of the diffracted light.

What are some common applications of diffraction gratings?

Diffraction gratings have many practical applications in various fields. They are commonly used in spectroscopy to analyze the composition of substances. They are also used in laser technology, as they can be used to filter out specific wavelengths of light. They are also used in astronomy to analyze the spectra of stars and other celestial objects.

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