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Homework Statement
The distance d from the center of the pattern to the location of the third diffraction minimum of the red laser is 4.05 centimeters. The wavelength of the red laser is 633 nanometers and the slit is 0.15 millimeters wide. How far is the screen from the slit?
Homework Equations
[tex]sin\theta = \frac{m\lambda}{a} [/tex]
The Attempt at a Solution
m = 3
[tex]\lambda = 633 \times 10^{-9} m [/tex]
[tex]a = 0.15 \times 10^{-3} m [/tex]
[tex]sin\theta = \frac{y}{4.05 \times 10^{-2} m}[/tex]
[tex]\frac{y}{4.05 \times 10^{-2} m} = \frac{m\lambda}{a}[/tex]
[tex]y = \frac{4.05 \times 10^{-2} m (3)(633 \times 10^{-9}m)}{0.15 \times 10^{-3} m}[/tex]
y = 0.00051273 m
[tex]sin\theta = \frac{0.00051273 m}{4.05 \times 10^-2 m}[/tex]
[tex]\theta = 0.725[/tex]
[tex]cos 0.725 = \frac{r}{4.05 \times 10^{-2}}[/tex]
[tex]r = 4.05 \times 10^{-2} \times cos 0.725[/tex]
[tex]r = 4.05 \times 10^{-2}[/tex]
This is not the correct answer. Where did I go wrong?
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