Complete Question
One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 2 cm across, and you estimate that the distance from the window shade to the wall is about 5 m.
Required:
Estimate the diameter of the pinhole.
Answer:
The diameter is [tex]d =0.000336 m[/tex]
Explanation:
From the question we are told that
The central maxima is [tex]D= 2cm = \frac{2}{100} = 0.02m[/tex]
The distance from the window shade is [tex]L = 5m[/tex]
The average wavelength of the sun is mathematically evaluated as
[tex]\lambda_{ave } = \frac{\lambda_i + \lambda_f}{2}[/tex]
Generally the visible light spectrum has a wavelength range between 400 nm to 700 nm
So the initial wavelength of the sun is [tex]\lambda _i = 400nm[/tex]
and the final wavelength is [tex]\lambda_f = 700nm[/tex]
Substituting this into the above equation
[tex]\lambda_{sun} = \frac{400nm +700nm}{2}[/tex]
[tex]= 550nm[/tex]
The diameter is evaluated as
[tex]d = \frac{2.44 \lambda_{sun} L}{D}[/tex]
substituting values
[tex]d = \frac{2.44 * 550*10^{-9} * 5 }{0.02}[/tex]
[tex]d =0.000336 m[/tex]
