Light from Element X through a diffraction Grating

[kikko]

Homework Statement

Light emitted by Element X passes through a diffraction grating having 1200 lines/mm. The diffraction pattern is observed on a screen 75.0 cm behind the grating. Bright fringes are seen on the screen at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. No other fringes are seen.

What is the maximum value of m for each of these diffracted wavelengths?
This part will be visible after you complete previous part(s).
What are the wavelengths of light emitted by Element X?

Homework Equations

[tex]\theta[/tex]_m = m([tex]\lambda/d[/tex]) (angles of bright fringes)
y_m = (m[tex]\lambda[/tex]L)/d
dsin[tex]\theta[/tex]_m = m[tex]\lambda[/tex]
y_m - Ltan[tex]\theta[/tex]_m

The Attempt at a Solution

\theta

No clue for this one. I tried plugging various things into the second equation, but got lost. I also don't understand how it can have multiple [tex]\lambda[/tex].

 

[kikko]

bump?

 

[SammyS]

What does each variable represent?

θ_m, m, λ, d, y_m, L

 

[SammyS]

Homework Statement

Light emitted by Element X passes through a diffraction grating having 1200 lines/mm. The diffraction pattern is observed on a screen 75.0 cm behind the grating. Bright fringes are seen on the screen at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. No other fringes are seen.

What is the maximum value of m for each of these diffracted wavelengths?
This part will be visible after you complete previous part(s).
What are the wavelengths of light emitted by Element X?

Homework Equations

[tex]\theta[/tex]_m = m([tex]\lambda/d[/tex]) (angles of bright fringes)
y_m = (m[tex]\lambda[/tex]L)/d
dsin[tex]\theta[/tex]_m = m[tex]\lambda[/tex]
y_m - Ltan[tex]\theta[/tex]_m

The Attempt at a Solution

\theta

No clue for this one. I tried plugging various things into the second equation, but got lost. I also don't understand how it can have multiple [tex]\lambda[/tex].

What is the range of wavelengths for the visible spectrum?

Find where the shortest wavelength (for the visible) would a appear on the screen, for m=1, m=2, ... until you can completely answer the first question.

 

[rwisz]

I would approach this problem by first understanding the concepts of diffraction and diffraction gratings. A diffraction grating is a device with many parallel slits or lines that can diffract light into a spectrum of colors. In this case, we are given that the diffraction grating has 1200 lines/mm, which means that it has a high resolution and can produce a detailed diffraction pattern.

To determine the maximum value of m for each of the diffracted wavelengths, we can use the equation dsin\thetam = m\lambda, where d is the distance between the lines on the grating, \theta is the angle of diffraction, and m is the order of the diffraction. We are given that the bright fringes are seen at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. This means that m can have values of 1, 2, and 3 respectively. Therefore, the maximum value of m for each of the diffracted wavelengths is 3.

To calculate the wavelengths of light emitted by Element X, we can use the equation ym = (m\lambdaL)/d, where ym is the distance from the central maximum, L is the distance from the grating to the screen, and d is the distance between the lines on the grating. We are given that L = 75.0 cm and d = 1/1200 mm. Plugging in the values for m and ym, we can solve for \lambda. The calculated wavelengths are 560 nm, 659 nm, and 935 nm for m = 1, 2, and 3 respectively.

In summary, the diffraction pattern observed on the screen is a result of the diffraction of light from Element X passing through the diffraction grating. The maximum value of m for each of the diffracted wavelengths is 3, and the wavelengths of light emitted by Element X are 560 nm, 659 nm, and 935 nm.