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A diffraction grating contains 15,000 lines/inch. We pass a laser beam through the grating. The wavelength of the laser is 633 nm. On a screen 2.66m away, we observe spots of light. (a) How far (m) from the central maximum (m = 0) is the first-order maximum (m = 1) observed? (b) How far (m) from the central maximum (m = 0) is the second-order maximum (m = 2) observed? DO NOT calculate this using the

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Answer:

Recall the Diffraction grating formula for constructive interference of a light

y = nDλ/w                                      Eqn 1

Where;

w = width of slit = 1/15000in =6.67x10⁻⁵in =   6.67x10⁻⁵ x 0.0254m = 1.69x10⁻⁶m

D = distance to screen  

λ = wavelength of light  

n = order number  = 1

Given  

y1 = ? from 1st order max to the central  

D = 2.66 m  

λ = 633 x 10-9 m  

and n = 1  

y₁ = 0.994m  

Distance (m) from the central maximum (n = 0) is the first-order maximum (n = 1)                =         0.994m

Q b. How far (m) from the central maximum (m = 0) is the second-order maximum (m = 2) observed?

w = width of slit = 1/15000in =6.67x10⁻⁵in =   6.67x10⁻⁵ x 0.0254m = 1.69x10⁻⁶m

D = distance to screen  

λ = wavelength of light  

n = order number  = 1

Given  

y1 = ? from 1st order max to the central  

D = 2.66 m  

λ = 633 x 10⁻⁹ m  

and n =  2

y₂ = 0.994m  

Distance (m) from the central maximum (n = 0) is the first-order maximum (n = 2) =1.99m