Diffraction Gratings This part will help you with the final section of Lab 8. Co

Question

Diffraction Gratings This part will help you with the final section of Lab 8. Consider a red laser of known wavelength lred incident on a diffraction grating with an unknown slit density, n (typically measured in slits/mm). Note that this means that the distance between two adjacent slits is d= 1/n. The central maximum occurs at angle -0. Do not assume the small angle approximation for these parts. e pattern is observed on a screen a distance L away from the diffraction grating and the distance between ximum and the first diffraction maximum is yred Save What is the angle of the first maximum. ed. In terms of1rd and L? Then plug in the numbers L-25 [2 points] cm, and yred 8.37 cm to find 6red in radians. [Hint: Use trigonometry! g) h) Solve for n (ord if you prefer) in terms of the variables nred and ed [2 points] in part (g) and ed Note that these are first-oder maxima.] Then plug in the answer you got Hint: Use the equation for the di raction grating marina! 635 nm to find n in slits/mm? The laser is now replaced with a green laser of unknown wavelength green and the distance between the central maximum and the first diffraction maximum on the screen is measured to be at angle reen- i) [1 point] Solve for green in terms ofOgreenAnd, and ned. The distance between the central maximum and the first diffraction maximum for the green laser, is measured to be green = 6.73 cm j [2 points] Find igreen in nm.

Explanation / Answer

part g:

use in Diffraction patterns

from triginometry

sin theta = Yred/Hypotenuse = Yred/L ( for smaller angles)

theta (red) = Yred/L ( formula) ----------------------1

in terms of numbers,

it is sin theta = 8.37cm/25 cm

sin theta = 0.3348

theta = 0.341 radians

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use d sin theta = n * W (wavelength)

n = d sin theta/W

n/d = sin theta/W

n/d = sin (0.341) /635*10^-9

n/d = 5.27 *10^5 slits/m

1mm = 10^-3 m

1m = 10^3 mm

n/d = 527.24 slits per mm

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i)

for Lgreen,

theta green = Ygreen/L

Subtitute from

theta green = ( Ygreen * theta red)/Y red

Ygreen = theta green * Yred/theta red

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j)

sin theta green = Ygreen * theta red/Yred

sin theta = 6.73 cm * 0.3348/8.37 cm

sin theta green = 0.254

now use d sin theta = nLgreen

Lgreen = (d/n) * sin theta

Lgreen = 0.254*10^-3 /(527.24 )

Lgreen =   481.75 nm

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