Section 8.15 Practice, Study, and Apply - Optics
Subsection Practice
The 3rd bright fringe of a double-slit interference pattern is 30.0 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 meters
Problem 8.15.2. Double-Slit II.
A 500 nm laser illuminates a double-slit apparatus with a slit separation distance of 7.73 \(\mu\)m. What is the angle (in degrees) from the horizontal to the 4th bright fringe?
Answer.
\(15^{\circ}\)
Problem 8.15.3. Double-Slit III.
A 680 nm laser illuminates a double-slit apparatus with a slit separation distance of 7.83 \(\mu\)m. On the viewing screen, you measure the distance from the central bright fringe to the 2nd bright fringe to be 88.2 cm. How far away (in meters) is the viewing screen from the double slits?
Answer.
5 meters
Problem 8.15.4. Single-Slit.
A laser of unknown wavelength is used to illuminate a single slit of width 100 \(\mu\)m. A viewing screen is placed 1.50 meters away from the slit. A measurement between the central bright fringe and the 2nd dark fringe yields a result of 1.95 cm. What is the wavelength (in nm) of the laser?
Answer.
650 nm
Problem 8.15.5. Angle of Refraction.
Light traveling from water enters a horizontal slab of glass. The light makes an angle of 20° with respect to the horizontal surface of the glass. The indexes of refraction for water and glass are \(n_{water} = 1.33\) and \(n_{glass} = 1.52\text{.}\) Calculate the angle of refraction (in degrees).
Answer.
\(55.3^{\circ}\)
Problem 8.15.6. Unknown Index of Refraction.
Light traveling from air strikes a horizontal slab of unknown material. The light makes an angle of 40° with respect to the perpendicular of the horizontal surface. The angle of refraction is measured to be about 29.4°. What is the index of refraction of this unknown material?
Answer.
1.31
Problem 8.15.7. Total Internal Reflection.
At what minimum incidence angle (in degrees) will you get total internal reflection of light that is traveling from water into a layer of ice? Note that \(n_{water} = 1.33\text{,}\) and \(n_{ice} = 1.31\text{.}\)
Answer.
\(80^{\circ}\)
Problem 8.15.8. Diverging Lens.
Consider a thin diverging lens with a focal length of 4 cm. A 2-cm-tall object is placed 8 cm in front of the lens. Use ray tracing to answer the following items:
- Estimate the image distance in cm.
- Estimate the image height in cm.
- Estimate the magnification
- Is the image real or virtual?
Problem 8.15.9. Magnifying Glass.
What is the focal length, in cm, of a magnifying glass (a thin converging lens) that produces a magnification of 3.00 when it is held 5.00 cm away from an object?
Answer.
7.5 cm
Subsection Study
A*R*C*S 8.15.1. Fun House Mirror.
You go to the hall of mirrors in a funhouse and stand 2.25 m in front of a spherical mirror. The mirror forms an image of you at a point 1.25 m behind the mirror. What is the focal length of the mirror?
Explanation 8.15.2. Ray Diagram.
Two objects and a mirror are arranged as shown below. Draw a ray diagram to determine the location of the image of each of the two objects.
Explanation 8.15.3. Single Slit.
A laser shines through a single slit of unknown width a. You observe at least one dark spot on a distant screen.Is the width of the slit greater than, less than, or equal to the wavelength of the laser?
Subsection Apply
Explanation 8.15.4. Ray Diagram.
A candle is located near two mirrors as shown in the figure below. Draw a ray diagram showing the location of the image that your eye sees when looking into the left mirror.
A*R*C*S 8.15.5. Human Eye.
The average human eye is about 2.4 cm in diameter, that is, the lens is 2.4 cm from the retina. Assume you have an average eye, and that an object that is 5.0 cm high is located 25 cm from your eye. What focal length must your lens be to create an image on your retina?
Tip.
Sensemaking suggestion: What type of lens is this? How can you tell?
References References
[1]
Practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.