- #1
Sarah Hallsway
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Homework Statement
A 600 line/mm diffraction grating is in an empty aquarium tank. The index of refraction of the glass walls is [n][/glass] = 1.50. A helium-neon laser (lambda=633 nm) is outside the aquarium. The laser beam passes through the glass wall and illuminates the diffraction grating.
a. What is the first order diffraction of the laser beam?
b. What is the first-order diffraction angle of the laser beam after the aquarium is filled with water? ([n][/water] = 1.33)
Homework Equations
Diffraction equation= m(lambda)=d(sin(theta1)+sin(theta2))
where m= diffraction order
d= grating spacing
theta 1= incident angle
theta 2= diffraction angle
and possibly Snell's law,
n1sin(theta1)=n2sin(theta2)
The Attempt at a Solution
My first try at a gave me the answer -41.80 degrees as the angle of diffraction. I assumed that the incoming angle (from the laser to the glass of the aquarium) was 90, then used snell's law to calculate the angle at which the laser bent, which was 41.81 degrees. I used 41.81 degrees in the diffraction gradient equation I provided above and got my theta2 to be equal to -41.80 degrees.
I know I probably went wrong assuming that the incoming angle was 90, and I also noticed that theta1 and theta2 were very similar which is not usually the case for diffraction gradient problems.
If someone could even just point me in the right direction, I would be very appreciative. For reference, the correct answers to this problem are a. 23.3 degrees and b. 16.6 degrees. Thank you in advance!