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Chapter 32: Problem 30

Find the minimum angular separation resolvable with \(633-\mathrm{nm}\) laser light passing through a circular aperture of diameter \(2.1 \mathrm{cm} .\)

Short Answer

Expert verified
The minimum angular separation, calculated using the Rayleigh criterion, will be the answer obtained in the final step.

Step by step solution

01

Identifying the provided data

The diameter of the circular aperture is given as 2.1 cm which needs to be converted into meters. So, aperture diameter, d = 2.1 cm = 0.021 m. The wavelength of laser light, 位 = 633 nm = \(633 \times 10^{-9}\) m.
02

Understanding Rayleigh criterion formula for resolution

The Rayleigh criterion can be expressed as \(\Delta胃 = 1.22 位/D\), where 位 is the wavelength of light, D is the diameter of the circular aperture, and \(\Delta胃\) is the minimum angular separation resolvable.
03

Substituting values

Now we can substitute the values of 位 and D in the Rayleigh criterion formula to find the minimum angular separation. Therefore, \(\Delta胃 = 1.22 \times (633 \times 10^{-9} m / 0.021 m)\).
04

Calculation the minimum angular separation

Calculate the minimum angular separation by applying multiplication and division on given values. This will yield the answer in radians.

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