A canvas tent has a single, tiny hole in its side. While inside the tent, you observe a dot on the wall of the tent, which is 2.0 m away (the dot is due to a distant point source of light of wavelength 550 nm). The dot has a diameter of 2.0 mm, and there is a faint ring around it. What is the size of the hole in the tent?
A) 0.55 mm
B) 0.67 mm
C) 1.10 mm
D) 1.34 mm

Question

Quizplus · Accepted Answer

We can use the formula for diffraction of light through a single slit:

sin(θ) = λ/d

where λ is the wavelength of light, d is the width of the slit, and θ is the angle between the straight-ahead direction and the first minimum of the diffraction pattern.

If we assume that the diameter of the dot on the wall is the diameter of the central maximum of the diffraction pattern, then we can use the formula:

D = 2 * (tan(θ/2)) * L

where D is the diameter of the central maximum, θ is the angle to the first minimum (which we just found), and L is the distance from the slit to the wall.

Plugging in the numbers:

θ = sin⁻¹(λ/d) = sin⁻¹(550 nm / d) 
D = 0.002 m 
L = 2.0 m

D = 2 * (tan(sin⁻¹(550 nm / d) / 2)) * 2.0 m

Solving for d:

d = 550 nm / sin(0.5 * tan⁻¹(D/4L))

Plugging in the numbers:

d = 550 nm / sin(0.5 * tan⁻¹(0.001 / 4*2.0))

d = 1.34 mm

Therefore, the size of the hole in the tent is 1.34 mm.

A Canvas Tent Has a Single, Tiny Hole in Its