Question

Consider two diffraction gratings with the same slit separation. The only difference between the two gratings is that one grating has 5 slits and the other 10 slits. Both gratings are illuminated with a beam of the same monochromatic light. Which of the following statements are true?
Check all that apply.
Check all that apply.
The grating with 5 slits produces the greater separation between peaks.
Both gratings produce peaks of the same width.
The grating with 10 slits produces the greater separation between peaks.
Both gratings produce the same separation between peaks.
The grating with 10 slits produces better-defined (narrower) peaks.
The grating with 5 slits produces better-defined (narrower) peaks.

Answer 1

Answer:

True The grid with more slits gives more angle separation increases

True. The grating with 10 slits produces better-defined (narrower) peaks

Explanation:

Such a system can be seen as a diffraction network in this case with different number of lines per unit length, the expression for the constructive interference of a diffraction network is

      d sin θ = m λ

where d is the distance between slits or lines, m the order of diffraction and λ the wavelength.

For network with 5 slits

      d = 1/5 = 0.2

For the network with 10 slits

      d = 1/10 = 0.1

let's calculate the separation (teat) for each one

      θ = sin⁻¹ (m λ / d)

for 5 slits

     θ₅ = sin⁻¹ (m λ 5)

for 10 slits

     θ₁₀ = sin⁻¹ (m λ 10)

we can appreciate that for more slits the angle increases

the intensity of a series of slits is

       I = I₀ sin²2 (N d/2) / sin² d/2)

when there are more slits (N) the peaks have greater intensity and are more acute (half width decreases)

let's analyze the claims

False

True The grid with more slits gives more angle separation increases

False

True The expression for the intensity of the diffraction peaks the intensity of the peaks increases with the number of slits as well as their spectral width decreases

False