Tippens Cap 33

ippens
Chapter 33. Light and Illumination

Light and the Electromagnetic Spectrum

33-1. An infrared spectrophotometer scans the wavelengths from 1 to 16 (m. Express these range in terms of the frequencies of the infrared rays.
[pic]
Range of frequencies: 1.88 x 1013 Hz to 30 x 1013 Hz

33-2. What is the frequency of violet light of wavelength 410 nm?
[pic] f = 7.32 x 1014Hz

33-3. A microwave radiator used in measuring automobile speeds emits radiation of frequency 1.2 x 109 Hz. What is the wavelength?
[pic] λ = 250 mm

33-4. What is the range of frequencies for visible light? ( Range of λ: 700 nm to 400 nm )
[pic]
Range of frequencies: 4.29 x 1014 Hz to 7.50 x 1014 Hz

33-5. If Plank’s constant h is equal to 6.626 x 10-34 J s, what is theenergy of light of wavelength 600 nm?
[pic] E = 3.31 x 10-19 J
33-6. What is the frequency of light whose energy is 5 x 10-19 J?
[pic] f = 7.55 x 1014 Hz

33-7. The frequency of yellow-green light is 5.41 x 1014 Hz. Express the wavelength of this light in nanometers and in angstroms?
[pic] λ = 555 nm
λ = 555 x 10-9 m(1 x 1010 A/m); λ = 5550 A

33-8. What isthe wavelength of light whose energy is 7 x 10-19 J?
[pic] λ = 284 nm

The Velocity of Light
33-9. The sun is approximately 93 million miles from the earth. How much time is required for the light emitted by the sun to reach us on earth?
[pic]; t = 8.33 min

33-10. If two experimenters in Galileo’s experiment were separated by a distance of 5 km, how much time would have passedfrom the instant the lantern was opened until the light was observed?
[pic] t = 17.0 x 10-6 s or 17.0 (s

33-11. The light reaching us from the nearest star, Alpha Centauri, requires 4.3 years to reach us. How far is this in miles? In kilometers?
s = ct = (186,000 mi/s)(3.154 x 107 s/yr)(4.30 yr); s = 2.53 x 1013 mi
s = ct = (3 x 108 m/s)(3.154 x 107 s/yr)(4.30 yr); s=4.07 x 1013 km

33-12. A spacecraft circling the moon at a distance of 384,000 km from the earth communicates by radio with a se on earth. How much time elapses between the sending and receiving of a signal?
s = (384,000 km)(1000 m/km) = 3.10 x 108 m; [pic]= 1.28 s
[pic] t = 133 s

33-13. An spacecraft sends a signal that requires 20 min to reach the earth. How far away is thespacecraft from earth?
s = ct = (3 x 108 m/s)(20 min)(60 s/min); s = 3.60 x 1011 m

Light Rays and Shadows
33-14. The shadow formed on a screen 4 m away from a point source of light is 60 cm tall. What is the height of the object located 1 m from the source and 3 m from the shadow?
Similar trianges:
[pic]
[pic] h = 2.40 m33-15. A point source of light is placed 15 cm from an upright 6-cm ruler. Calculate the length of the shadow formed by the ruler on a wall 40 cm from the ruler.
[pic] h = 22.0 cm

33-16. How far must an 80-mm-diameter plate be placed in front of a point source of light if it is to form a shadow 400 mm in diameter at a distance of 2 m from the light source?
[pic]x = 400 mm


33-17. A source of light 40 mm in diameter shines through a pinhole in the tip of a cardboard box 2 m from the source. What is the diameter of the image formed on the bottom of the box if the height of the box is 60 mm?
[pic] y = 1.20 mm

*33-18. A lamp is covered with a box, and a 20-mm-long narrow slit is cut in the box so that light shines through. An object 30mm tall blocks the light from the slit at a distance of 500 mm. Calculated the length of the umbra and penumbra formed on a screen located 1.50 m from the slit. (Similar Δ’s)
[pic]
[pic]; u = 50 mm
[pic] from which p = 130 mm
Illumination of Surfaces
33-19. What is the solid angle subtended at the center of a 3.20-m-diameter sphere by a 0.5-m2 area on its...