Calculate the width of the central maximum for the 0.04 mm slit assuming all other dimensions remain the same.

Question

Assume that you had used an argon laser (wavelength = 488 nm) instead of the HeNe laser. Calculate the width of the central maximum for the 0.04 mm slit assuming all other dimensions remain the same.

Answer 1

If you want to measure the width of the central maximum in the diffraction pattern on a screen, you would need the distance from the diffraction slit and the screen (let's call it L)

The edge of the central maximum will in effect be defined by the first minimum on either side of the central maximum at which point the light intensity goes to zero. in the case of single slit diffraction, if the angle between the line from the slit to a point on the screen directly in front of the slit and line from the slit to the location of a minima is θ, d is the width of the slit and λ is the wavelength of the light, the formula will be

dsinθ = mλ where m is going to be an integer.

for the first minima, m will be 1

so

dsinθ = λ

and so in our case here,

sinθ = (λ/d) = (488 nm)/(0,04 mm) = (4.88 x 10^-7 m)/(4.0 x 10^-5 m) = 1.22 x 10^-2

θ = 0.699⁰

Now, if you have a value for the distance between the slit and the screen (L), the distance from the center of the central maximum to the first minimum on either side will be equal to Ltanθ, so the width of the central maximum would be twice that

2Ltanθ or 2Ltan( 0.699⁰)

single slit diffraction, the width of the