# Need help with a diffractiongrating problem.

• seanmcgowan
Then theta is about 4.6 degrees, or about 0.08 rad.In summary, the problem involves finding the second order angle of diffraction for light with a wavelength of 400nm passing through a 1.00x10^4 lines/cm diffraction grating. Using the equation d*sin(theta) = m*wavelength, and the correct value of d being 10^-6m, the angle was calculated to be approximately 4.6 degrees or 0.08 radians. The previous incorrect value of d resulted in an incorrect answer.
seanmcgowan

## Homework Statement

Light with a wavelength of 400nm passes through a 1.00x10^4 lines/cm diffraction grating. What is the second order angle of diffraction?

a) 21.3 c)56.5
b) 53.1 d) 72.1

## Homework Equations

d*sin(theta)=m* wavelength

## The Attempt at a Solution

I rearranged the equation to: Theta= sin^-1({wavelength*order}/ d)
Theta= sin^-1 (4*10^-7*2/{1/1*10^2)= sin^-1(8*10^-9)= 4.58366

Obviously, this isn't the answer. Could someone show me how to figure these problems out? I have a test coming up and i am completely stumped on all of these types of questions.

Theta= sin^-1 (4*10^-7*2/{1/1*10^2)= sin^-1(8*10^-9)= 4.58366

Here d = 0.01/1x10^4 m or 10^-6 m.

Ok i reworked the problem, and got a different answer, but it is still no where near any of the multiple choice answers! what am I doing wrong?

Can you show your second calculation, with the new value of d? Otherwise we can't see what's wrong.

EDIT:

4*10^-7*2/(1/1*10^2) = 8*10^-9

There is an error here, besides the incorrect value of d. Do you see it?

Holly cow! I just re-reworked the problem for about the hundredth time and got the answer of 53.1, which is actually one of my choices! and I should imagine that the (8*10^-9) is wrong. The answer should be 8*10^-1. Right? or am I STILL messing up?

Yes, it is 0.8 using the correct value of d=10-6m.

Or, if d=(1/102)m or 10-2m as you had earlier, you should have gotten 8x10-5 for the expression.

## 1. What is a diffraction grating?

A diffraction grating is a scientific instrument that splits a beam of light into its different wavelengths, similar to a prism. It consists of a series of closely spaced parallel lines or grooves on a surface, which act as a series of parallel slits and cause diffraction of the light passing through them. This results in a pattern of bright and dark fringes, allowing for the analysis of the light's wavelength and intensity.

## 2. How do I use a diffraction grating?

To use a diffraction grating, you will need to align the grating with the light source and a detector, such as a screen or a spectrometer. The light will pass through the grating and form a diffraction pattern on the detector, which can then be analyzed to determine the wavelength and intensity of the light. The angle of the grating and the distance between the lines will also affect the pattern, so careful adjustments may be necessary.

## 3. What is the equation for diffraction grating?

The equation for diffraction grating is nλ = d(sinθi + sinθm), where n is the order of diffraction, λ is the wavelength of light, d is the distance between the lines on the grating, θi is the angle of incidence, and θm is the angle of diffraction. This equation is derived from the principles of diffraction and can be used to calculate the wavelength of light passing through a diffraction grating.

## 4. What are some common applications of diffraction gratings?

Diffraction gratings are used in a variety of scientific and technological applications, including spectroscopy, optical instruments, and telecommunications. They are also commonly used in astronomy to analyze the light emitted by celestial objects and determine their composition and distance. Diffraction gratings are also used in the production of holograms and in the study of crystal structures.

## 5. What factors can affect the performance of a diffraction grating?

The performance of a diffraction grating can be affected by several factors, including the quality and spacing of the lines on the grating, the angle and alignment of the grating, and the wavelength and intensity of the light being diffracted. Environmental factors such as temperature and humidity can also affect the performance of a diffraction grating. Additionally, the presence of imperfections or defects on the surface of the grating can also impact its performance.

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