Final answer:
To find the intensity at a 10° angle for a single slit illuminated by 576 nm wavelength light, one must use the single-slit diffraction formula which incorporates the width of the slit, the wavelength of the light, and the angle in question.
Step-by-step explanation:
To find the intensity at a 10° angle to the axis in terms of the intensity of the central maximum for a single slit diffraction pattern, we would use the single-slit diffraction formula, which states:
I(\theta) = I_0 \left( \frac{\sin(\beta)}{\beta} \right)^2
where:
- I(\theta) is the intensity at an angle \( \theta \)
- I_0 is the intensity of the central maximum
- \( \beta = \frac{\pi a \sin(\theta)}{\lambda} \)
- a is the width of the slit
- \( \lambda \) is the wavelength of the light
Substituting the given values into the equation:
\( a = 0.10 \, \text{mm} = 1 \times 10^{-4} \text{m} \)
\( \lambda = 576 \, \text{nm} = 576 \times 10^{-9} \text{m} \)
\( \theta = 10^\circ = \frac{10 \pi}{180} \text{rad} \)
Then calculate \( \beta \) and use it to find I(\theta) in terms of I_0. Note that you may need to use a calculator to compute the sine function and squared term, and also understand that the exact value of I(\theta) will depend on the interference pattern created by the slit and the wave nature of the light.