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.
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?
f = 7.32 x 1014 Hz
33-3.A microwave radiator used in measuring automobile speeds emits radiation of frequency 1.2 x 109 Hz. What is the wavelength?
= 250 mm
33-4. What is the range of frequencies for visible light? ( Range of : 700 nm to 400 nm )
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 the energy of light ofwavelength 600 nm?
E = 3.31 x 10-19 J
33-6. What is the frequency of light whose energy is 5 x 10-19 J?
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?
= 555 nm
= 555 x 10-9 m(1 x 1010 A/m); = 5550 A
33-8. What is the wavelength of light whose energyis 7 x 10-19 J?
= 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?
; 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 passed from the instant the lantern was openeduntil the light was observed?
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 circlingthe 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; = 1.28 s
t = 133 s
33-13. An spacecraft sends a signal that requires 20 min to reach the earth. How far away is the spacecraft from earth?
s = ct = (3 x 108 m/s)(20 min)(60s/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?
h = 2.40 m
33-15. 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.
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?
x = 400 mm
33-17. A source of light 40 mm in diameter shines through a pinhole in the tip of acardboard 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?
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 30 mm tall blocks the light from the slit at a distance of 500 mm. Calculated the length of the umbra and penumbraformed on a screen located 1.50 m from the slit. (Similar ’s)
; u = 50 mm
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 surface?
= 0.195 sr
33-20. A solid angle of 0.080 sr is subtended at the center of a 9.00 cm diameter sphere by surface...