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 4 m.

Estimate:
a. The average wavelength of the sunlight (in nm)
b. The diameter of the pinhole (in mm).

Answer 1

Given that,

Central maximum = 1 cm

Distance from the window shade to the wall =4 m

We know that,

The visible range of the sun light is 400 nm to 700 nm.

(a). We need to calculate the average wavelength

Using formula of average wavelength

`\lambda_(avg)=(\lambda_(1)+\lambda_(2))/(2)`

Put the value into the formula

`\lambda_(avg)=(400+700)/(2)`

`\lambda_(avg)=550\ nm`

(b). We need to calculate the diameter of the pinhole

Using formula for diameter

`w=(2.44\lambda L)/(D)`

`D=(2.44\lambda L)/(w)`

Put the value into the formula

`D=(2.44*550*10^(-9)*4)/(1*10^(-2))`

`D=0.537\ mm`

Hence, (a). The average wavelength 550 nm.

(b). The diameter of the pinhole is 0.537 mm.