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 1 cm across, and you estimate that the distance from the window shade to the wall is about 3 m . Estimate (a) the average wavelength of the sunlight (in nm) and (b) the diameter of the pinhole (in mm).

Answer 1

Answer:

a)$\lambda _{avg}=550 nm$

b)D=0.402 mm

Explanation:

We know that visible range of sun light is 400 nm to 700 nm.

So the average wavelength

$\lambda _{avg}=\dfrac{\lambda _1+\lambda _2}{2}$

$\lambda _{avg}=\dfrac{400+700}{2}$

$\lambda _{avg}=550 nm$

To find the diameter

We know that the relation

$D=\dfrac{2.44\lambda L}{w}$

Where D=Diameter of pin hole

          λ=Average wavelength

           w=Central distance

        L=length

So now by putting the values

$D=\dfrac{2.44\times 550\times 10^{-9}\times 3}{0.01}$

D=0.402 mm