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Chapter 36: Q98P (page 1115)

Suppose that two points are separated by 2.0 cm. If they are viewed by an eye with a pupil opening of 5.0 mm, what distance from the viewer puts them at the Rayleigh limit of resolution? Assume a light wavelength of 500 nm.

Short Answer

Expert verified

The required distance is 164 m.

Step by step solution

01

Describe the diffraction by a circular aperture or a lens

The expression to calculate the distance between the eye and two objects is given by,

sinθ=1.22λd

Here, λ is the wavelength, d is diameter, and θ is angle.

Let D be the distance between two objects, and L be the distance between the eye and two objects. Then,

Lθ=Dθ=DL

From the above equation,

θ=1.22λdDL=1.22λdL=Dd1.22λ ….. (1)

02

Determine the distance between the eye and two objects

Substitute 500×10-9m for λ, 5.0×10-3m for d, and 2.0×10-2m for D in equation (1).

L=2.0×10-2m5.0×10-3m1.22500×10-9m=164m

Therefore, the required distance is 164 m.

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