After pulling down your window shade, 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 3 cm across, and you estimate that the distance from the window shade to the wall is about 3 m . Estimate the diameter of the pinhole (in mm).

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2022-08-16

After pulling down your window shade, 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 3 cm across, and you estimate that the distance from the window shade to the wall is about 3 m .
Estimate the diameter of the pinhole (in mm).

Answer & Explanation

Kody Larsen

Kody Larsen

Beginner2022-08-17Added 11 answers

Given data:
Dentral distance, v=3 cm=0.03 m
Distance from the window shade to the wall, D=3 m
Visible range of wavelength of sunlight, 400 nm to 700 nm
Wavelength of sunlight λ = 500   n m = 500 × 10 9   m (assumed)
The formula of central distance:
w = 2.44 λ D d
where,
d=Diameter
d = 2.44 λ D w
Plugging in the given values:
d = 2.44 × 500 × 10 9 × 3 0.03 = 122 000 × 10 9 = 0.122 × 10 3   m = 0.122   m m
Answer:
Diameter of pinhole: 0.122 mm

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