Lightsorce through spectrometer

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A light beam directed at a spectrometer with a grating of 300 slits/mm shows coinciding red and blue lines at a deflection angle of 24.5°. The calculated distance between slits (d) is 3.33 x 10^-6 m. The wavelengths for red and blue light were initially calculated as 625 nm and 500 nm, respectively, with an incorrect order of n values. It was clarified that n must be an integer, leading to the conclusion that red should correspond to n=2 and blue to n=3, resulting in revised wavelengths of approximately 690 nm for red and 461 nm for blue. The discussion emphasizes the importance of using integer values for n in diffraction calculations.
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Homework Statement


A light hits a spektrometer perpendicular into a gitter with 300 slits/mm. You observes that a red and a blue line (in Visual light) coinciding. And the angle deflectionis 24.5°. What wavelenght have the red and the blue lines.
No n is given.

Homework Equations


d*sinα=n*λ

The Attempt at a Solution


First i calculated d
1/300000m = 3.33*10-6
((3.33*10-6)*(sin24.5))/625-9 http://www.dramaten.se/Repertoar/-Ungefar-lika-med/ 2.5

((3.33*10-6)*(sin24.5))/500-9 http://www.dramaten.se/Repertoar/-Ungefar-lika-med/ 2.5

Answer:
so the red wavelenght is 625nm
so the blue wavelenght is 500nm
n=2.5

Is this correct ? can it be 2.5?? the blue is closer to n3 and red n2
 
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SwedishFred said:

Homework Statement


A light hits a spektrometer perpendicular into a gitter with 300 slits/mm. You observes that a red and a blue line (in Visual light) coinciding. And the angle deflectionis 24.5°. What wavelenght have the red and the blue lines.
No n is given.

Homework Equations


d*sinα=n*λ

The Attempt at a Solution


First i calculated d
1/300000m = 3.33*10-6
((3.33*10-6)*(sin24.5))/(625*10-9) http://www.dramaten.se/Repertoar/-Ungefar-lika-med/ 2.5 , (I get ≈ 2.2)

((3.33*10-6)*(sin24.5))/(500*10-9) http://www.dramaten.se/Repertoar/-Ungefar-lika-med/ 2.5 , (I get ≈ 2.7)

Answer:
so the red wavelenght is 625nm
so the blue wavelenght is 500nm
n=2.5

Is this correct ? can it be 2.5?? the blue is closer to n3 and red n2
So, I take it that "gitter" is "grating".

I get approximately 2.2 and 2.7 as shown above in RED.

So, yes, use n = 2 for red & n = 3 for blue.
 
Hello, SwedishFred.

You know that n must be an integer, so n cannot be 2.5. Think about this: Is it possible for two different wavelengths to overlap using the same value of n for each wavelength?
 
TSny said:
Hello, SwedishFred.

You know that n must be an integer, so n cannot be 2.5. Think about this: Is it possible for two different wavelengths to overlap using the same value of n for each wavelength?
No that was what i was thinking about, so I understand it now, its much easier to see it happened ;-)
Thanx
 
SwedishFred said:
No that was what i was thinking about, so I understand it now, its much easier to see it happened ;-)
Thanx
What do you get for the two wavelengths?
 
((3.33*10-6)*(sin24.5))/2
((3.33*10-6)*(sin24.5))/3
Red 690nm
Blue 461nm

True ?
 
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