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 cmcm across, and you estimate that the distance from the window shade to the wall is about 5 mm.

Required:
Estimate the diameter of the pinhole.

Answer 1

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
`d =0.000336 m`

Step-by-step explanation:

From the question we are told that

The central maxima is
`D= 2cm = (2)/(100) = 0.02m`

The distance from the window shade is
`L = 5m`

The average wavelength of the sun is mathematically evaluated as

`\lambda_(ave ) = (\lambda_i + \lambda_f)/(2)`

Generally the visible light spectrum has a wavelength range between 400 nm to 700 nm

So the initial wavelength of the sun is
`\lambda _i = 400nm`

and the final wavelength is
`\lambda_f = 700nm`

Substituting this into the above equation

`\lambda_(sun) = (400nm +700nm)/(2)`

`= 550nm`

The diameter is evaluated as

`d = (2.44 \lambda_(sun) L)/(D)`

substituting values

`d = (2.44 * 550*10^(-9) * 5 )/(0.02)`

`d =0.000336 m`