# Homework Help: 2 Slit Diffraction

1. Apr 6, 2005

### stunner5000pt

A coherent, monochromatic HeNe laser beam 1cm in diameter at lambda = 634nm illuminates a pair of slits. The separation of the slits is 2mm and the slits are each 0.1mm across. An interference pattern is cast on a screen 1m away from the slits. Index of refraction of air = 1.0002926 and CO2 (at STP) = 1.000449.

Find the location of the central maximimum and the 1st 2nd and 10th maxima
Now normally this isnt a big deal all i use is the formula
$$sin \theta = \frac{m \lambda}{d}$$ and $$\frac{\Delta x}{L} = \frac{\lambda}{d}$$
d = 2.1mm
lambda = 634nm
L = 1m
the thing which throws me off is the diameter of the beam. Does that have any effect on the way this pattern appears??

b) Find the intensity of the 10 th maximum compared to the intensity of the central maximum

using this formula $$I(\theta) = I_{m} (cos^2 \beta) (\frac{sin \alpha}{\alpha})^2$$
where $$\alpha = \frac{\pi a}{\lambda} sin \theta$$
$$\beta = \frac{\pi a}{\lambda} sin \theta$$
and a = width of slit = 0.1mm
for the central max the angle theta is zero and for the 10th the angle is determined from above

c) Now the room is filled with CO2 uniformly. What is the index of refraction of the Co2 gas? In three sentence or less explain how the intensity of the pattern will change

well since carbon di oxide has a different index of refraction (which is 1.000449)
should i use this little relation
$$\frac{n_{air}}{n_{CO_{2}}} = \frac{v_{CO_{2}}}{v_{air}}$$
and this is also the reation of the wavelengths and the frequencies so equate them all

Please tell me if im wrong, i quite stumped on the width of the beam... How would i deal with that??

2. Apr 6, 2005

### stunner5000pt

can anyone help??

my only problem is what to do width the width of the beam?? Any help would be greatly appreciated!!!!!!!!