Calculating Third-Order Maximum Angle for Grating

In summary, the purpose of calculating the third-order maximum angle for grating is to determine the angular position of the maximum intensity of light diffracted by the grating. The calculation can be done using the equation θ = sin^-1(mλ/d), where θ is the maximum angle, m is the diffraction order, λ is the wavelength of light, and d is the spacing between grating lines. The diffraction order refers to the number of times light diffracts from the grating and the spacing between grating lines plays a role in determining the amount of diffraction. The third-order maximum angle can be calculated for all types of diffraction gratings as long as the grating period is known and the light
  • #1

Homework Statement



A grating has exactly 7000 lines uniformly spaced over 2.67 cm and is illuminated by light from a mercury vapor discharge lamp. What is the expected angle for the third-order maximum of the green line ( = 546 nm)?

Homework Equations



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The Attempt at a Solution



no idea :(
 
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  • #2
Try to find out the relevant equation for diffraction grating.
 
  • #3


I would suggest using the formula for calculating the angle of diffraction for a grating, which is given by:

sinθ = mλ/d

Where θ is the angle of diffraction, m is the order of the maximum, λ is the wavelength of the light, and d is the spacing between the lines on the grating.

In this case, we know that the green line has a wavelength of 546 nm and the grating has 7000 lines over a distance of 2.67 cm. So, plugging in the values, we get:

sinθ = (3)(546 nm)/(7000 lines)(2.67 cm)

Solving for θ, we get:

θ = 0.035 radians

To convert to degrees, we multiply by 180/π, giving us an angle of approximately 2.01 degrees.

Therefore, the expected angle for the third-order maximum of the green line is approximately 2.01 degrees.
 

What is the purpose of calculating third-order maximum angle for grating?

The third-order maximum angle for grating is used to determine the angular position at which the maximum intensity of light diffracted by the grating will occur. This information is important for designing optical systems and analyzing the performance of diffraction gratings.

How is the third-order maximum angle for grating calculated?

The third-order maximum angle for grating can be calculated using the equation: θ = sin^-1(mλ/d), where θ is the maximum angle, m is the diffraction order, λ is the wavelength of light, and d is the spacing between grating lines.

What is the diffraction order in the calculation of third-order maximum angle for grating?

The diffraction order refers to the number of times the light diffracts from the grating. In this case, the third-order maximum angle corresponds to the third diffraction order.

What is the significance of the spacing between grating lines in the calculation?

The spacing between grating lines, also known as the grating period, determines the amount of diffraction that occurs. A smaller spacing results in a larger diffraction angle, while a larger spacing results in a smaller diffraction angle.

Can the third-order maximum angle for grating be calculated for all types of diffraction gratings?

Yes, the third-order maximum angle can be calculated for all types of diffraction gratings as long as the grating period is known and the light being used falls within the grating's usable wavelength range.

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