How Does Wavelength Affect Intensity in a Double Slit Experiment?

[navm1]

Homework Statement

Coherent light with wavelength 585 nm passes through two very narrow slits that are
0.320 mm apart. The screen is 0.700 m away from the slits. The intensity is I0 at the
centre of the central maximum (theta=0)

(a) What is the phase difference (in radians) in the light from the two slits at an angle
of 23degrees from the centre line?

(b) What is the distance on the screen from the centre of the central maximum to the
point where the intensity has dropped to I0/2?

Homework Equations

Φ=2π/λ*dθ
I=I_0*cos²Φ/2

The Attempt at a Solution

a)
(2pi*3.2x10^-4)/(5.85x10^-7)*23pi/180=439pi radians

b) I=I_0cos^2(Φ/2)

cos^2((pi/2)/2)=1/2

So i figured Φ=2pi but the equation i wanted to use to solve is

Φ=(2*pi*d)/(λ)*θ

but i don't have a theta. For part a it was 23 but i figured there will be a completely new angle for this part of the question.

Thanks

 

[mfb]

but i don't have a theta

Well, you have to calculate it with that formula.
You can get Φ with first equation you have in (b). It is not 2 pi (plug it in and see if the result would be right).

 

[navm1]

Well, you have to calculate it with that formula.
You can get Φ with first equation you have in (b). It is not 2 pi (plug it in and see if the result would be right).

i meant to put pi sorry.

d is slit separation right? i think i was getting mixed up and thinking it was distance from screen to centre

 

[mfb]

Looks like slit separation in your formula.

Pi is still wrong. Please stop guessing and calculate the value.