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Learning Introductory Physics with Activities

Section 19.7 Practice - Physical Optics

Subsubsection Explanation Practice

Explanation 19.7.1. Two Sources.

The source in the double slit experiment emits at two wavelengths, \(\lambda_1\) and \(\lambda_2\text{.}\) On the viewing screen, the fourth maximum for \(\lambda_1\) is located at the same spot as the fifth maximum for \(\lambda_2\text{.}\) Explain how this is possible and determine the correct ratio of the wavelengths.

Subsubsection A*R*C*S Practice

A*R*C*S 19.7.2. Single Slit Pattern.

A \(650 \mathrm{~nm}\) laser illuminates a single slit and is observed on a screen \(1.2 \mathrm{~m}\) behind the slit. The distance between the second minimum on the right and the second minimum on the left is \(11 \mathrm{~mm}\text{.}\) What is the width of the slit?

A*R*C*S 19.7.3. Minimum Separation.

Suppose that the highest order fringe that can be observed is the eighth in a double-slit experiment where 550-nm wavelength light is used. What is the minimum separation of the slits?

Subsubsection Numerical Practice

Calculation 19.7.4. Double-Slit I.

The 3rd bright fringe of a double-slit interference pattern is \(30.0 \mathrm{~cm}\) above the central bright fringe. If the angle from the horizontal (the central bright fringe) to this 3rd bright fringe is \(12.0\) degrees, what is the distance (in meters) between the double slits and the viewing screen?
Answer.
\(1.41 \mathrm{~m}\)

Calculation 19.7.5. Double-Slit II.

A \(500 \mathrm{~nm}\) laser illuminates a double-slit apparatus with a slit separation distance of \(7.73 \mathrm{~\mu m}\text{.}\) What is the angle (in degrees) from the horizontal to the 4th bright fringe?
Answer.
\(15^{\circ}\)

Calculation 19.7.6. Double-Slit III.

A \(680 \mathrm{~nm}\) laser illuminates a double-slit apparatus with a slit separation distance of \(7.83 \mathrm{~\mu m}\text{.}\) On the viewing screen, you measure the distance from the central bright fringe to the 2nd bright fringe to be \(88.2 \mathrm{~cm}\text{.}\) How far away (in meters) is the viewing screen from the double slits?
Answer.
\(5 \mathrm{~m}\)

Calculation 19.7.7. Single-Slit.

A laser of unknown wavelength is used to illuminate a single slit of width \(100 \mathrm{~\mu m}\text{.}\) A viewing screen is placed \(1.50 \mathrm{~m}\) away from the slit. A measurement between the central bright fringe and the 2nd dark fringe yields a result of \(1.95 \mathrm{~cm}\text{.}\) What is the wavelength (in nm) of the laser?
Answer.
\(650 \mathrm{~nm}\)

References References

[1]
Numerical practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.