How to Calculate the Width of Slits in a Diffraction Grating Experiment?

[mrbling]

Question: A set of narrow vertical slits is located a distance D from a screen. The slits are equally spaced and have the same width. The intensity pattern in the figure is observed when light from a laser passes through the slits, illuminating them uniformly. The screen is perpendicular to the direction of the light.


Calculate the width of the slits, in micrometers.

You are given the following data: Distance to the screen = 2.77 meters; Wavelength of light = 0.420 micrometers; Distance between tick marks on the intensity figure = 1.60 cm (The figure has the generic diffraction grating light pattern, with tick marks occurring between each maxima)

Maxima occur at sin theta = m lambda / d (where m is the order, lambda is the wavelength of light, and d is the distance between slits)

first.. I find out what theta is.. i can find this by
tan theta = (.016m)/(2.77m)
tan theta = .0057761
theta = .33095 degrees

plugging into the maxima formula,
sin theta = m lambda / d
sin (.33095) = 1 (.420x10^-6) / d
d = 7.27x10^-5m = 72.7 micrometers

72.7 micrometers is incorrect. Anyone know where I went wrong?

Thanks.

 

[mrbling]

Any thoughts on this problem?

It seems so straight forward that I can't see where I may have gone wrong..

Thanks..

 

[M98Ranger]

It looks like you made a small error in your calculation for theta. The correct value for theta is actually 0.33095 radians, not degrees. So the correct calculation would be:

sin(0.33095) = 1(0.420x10^-6) / d
d = 7.27x10^-5 m = 72.7 micrometers

Therefore, the width of the slits would be approximately 72.7 micrometers. It is always important to double check your units and make sure you are using the correct values for your calculations. In this case, converting from radians to degrees caused the error in your result.