College Physics: A Strategic Approach Technology Update, Books A La Carte Edition (3rd Edition)
College Physics: A Strategic Approach Technology Update, Books A La Carte Edition (3rd Edition)
3rd Edition
ISBN: 9780134143774
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Textbook Question
Chapter 17, Problem 1CQ

The frequency of a light wave in air is 5.3 × 1014 Hz. Is the frequency of this wave higher, lower, or the same after the light enters a piece of glass?

Expert Solution & Answer
Check Mark
To determine

To find: The frequency of light wave is higher, lower or the same after the light enters a piece of glass.

Answer to Problem 1CQ

The frequency of light wave is same after the light enters a piece of glass.

Explanation of Solution

Given data:

The frequency of light wave is 5.3×1014Hz .

Formula used:

Write the expression for refractive index.

n=cv (1)

Here,

n is index of refraction,

c is the speed of light in vacuum, and

v is the speed of light in a material.

Write the expression for speed.

v=fλ (2)

Here,

f is the frequency, and

λ is wavelength.

Explanation:

Draw the light wave travels from air to glass as shown in Figure 1.

College Physics: A Strategic Approach Technology Update, Books A La Carte Edition (3rd Edition), Chapter 17, Problem 1CQ

Refer to Table 17.1 in the textbook, the value of index of refraction for glass and air is 1.50 and 1.0003 respectively.

Modify equation (1) for air as follows.

nair=cvair (3)

Modify equation (2) for air as follows.

vair=fairλair

Substitute fairλair for vair in equation (3),

nair=cfairλair

Rearrange the equation.

λair=cnairfair (4)

Modify equation (1) for glass as follows.

nglass=cvglass (5)

Modify equation (2) for air as follows.

vglass=fglassλglass

Substitute fglassλglass for vglass in equation (5),

nglass=cfglassλglass

Rearrange the equation as follows.

λglass=cnglassfglass (6)

Here, the value of c is 3×108ms .

Substitute 3×108ms for c , 1.0003 for nair and 5.3×1014Hz for fair in equation (4),

λair=3×108ms(1.0003)(5.3×1014Hz)=5.65×107m5.7×107m

Substitute 3×108ms for c , 1.5 for nglass and 5.3×1014Hz for fglass in equation (6),

λglass=3×108ms(1.5)(5.3×1014Hz)=3.7×107m

Find the value of nairλair .

nairλair=(1.0003)(5.7×107m)=5.701×107m5.7×107m

Find the value of nglassλglass .

nglassλglass=(1.5)(3.7×107m)=5.55×107m5.6×107m

Write the relation between nairλair and nglassλglass using obtained values.

nairλairnglassλglass

Re-arrange equation (4) as follows.

fair=cnairλair (7)

Re-arrange equation (6) as follows.

fglass=cnglassλglass (8)

Divide equation (7) by (8).

fairfglass=(cnairλair)(cnglassλglass)=nglassλglassnairλair

Substitute nglassλglass for nairλair ,

fairfglass=nglassλglassnglassλglassfairfglass=1fair=fglass

Conclusion:

Hence, the frequency of light wave is same after the light enters a piece of glass.

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02:42

Chapter 17 Solutions

College Physics: A Strategic Approach Technology Update, Books A La Carte Edition (3rd Edition)

Ch. 17 - Light with a wavelength of 600 nm is incident on a...Ch. 17 - White light is incident on a diffraction grating....Ch. 17 - Figure Q17.13 shows a light wave incident on and...Ch. 17 - A soap bubble usually pops because some part of it...Ch. 17 - An oil film on top of water has one patch that is...Ch. 17 - Should the antireflection coating of a microscope...Ch. 17 - Example 17.5 showed that a thin film whose...Ch. 17 - Prob. 18CQCh. 17 - Prob. 19MCQCh. 17 - The frequency of a light wave in air is 4.6 1014...Ch. 17 - Light passes through a diffraction grating with a...Ch. 17 - Blue light of wavelength 450 nm passes through a...Ch. 17 - Yellow light of wavelength 590 nm passes through a...Ch. 17 - Light passes through a 10-m-wide slit and is...Ch. 17 - Prob. 25MCQCh. 17 - You want to estimate the diameter of a very small...Ch. 17 - Prob. 1PCh. 17 - a. How long (in ns) does it take light to travel...Ch. 17 - A 5.0-cm-thick layer of oil (n = 1.46) is...Ch. 17 - A light wave has a 670 nm wavelength in air. Its...Ch. 17 - How much time does it take a pulse of light to...Ch. 17 - A helium-neon laser beam has a wavelength in air...Ch. 17 - Two narrow slits 50 m apart are illuminated with...Ch. 17 - Light from a sodium lamp (= 589 nm) illuminates...Ch. 17 - Two narrow slits are illuminated by light of...Ch. 17 - A double-slit experiment is performed with light...Ch. 17 - Light from a helium-neon laser (= 633 nm) is used...Ch. 17 - Two narrow slits are 0.12 mm apart. Light of...Ch. 17 - In a double-slit experiment, the distance from one...Ch. 17 - A diffraction grating with 750 slits/mm is...Ch. 17 - A 1.0-cm-wide diffraction grating has 1000 slits....Ch. 17 - Light of wavelength 600 nm illuminates a...Ch. 17 - A lab technician uses laser light with a...Ch. 17 - The human eye can readily detect wavelengths from...Ch. 17 - A diffraction grating with 600 lines/mm is...Ch. 17 - A 500 line/mm diffraction grating is illuminated...Ch. 17 - What is the thinnest film of MgF2 (n = 1.38) on...Ch. 17 - A very thin oil film (n = 1.25) floats on water (n...Ch. 17 - A film with n = 1.60 is deposited on glass. What...Ch. 17 - Antireflection coatings can be used on the inner...Ch. 17 - Solar cells are given antireflection coatings to...Ch. 17 - A thin film of MgF2 (n = 1.38) coats a piece of...Ch. 17 - Looking straight downward into a rain puddle whose...Ch. 17 - A helium-neon laser (= 633 nm) illuminates a...Ch. 17 - For a demonstration, a professor uses a razor...Ch. 17 - A 0.50-mm-wide slit is illuminated by light of...Ch. 17 - The second minimum in the diffraction pattern of a...Ch. 17 - What is the width of a slit for which the first...Ch. 17 - A 0.50-mm-diameter hole is illuminated by light of...Ch. 17 - Light from a helium-neon laser (= 633 nm) passes...Ch. 17 - You want to photograph a circular diffraction...Ch. 17 - Infrared light of wavelength 2.5 m illuminates a...Ch. 17 - An advanced computer sends information to its...Ch. 17 - Figure P17.38 shows the light intensity on a...Ch. 17 - Figure P17.38 shows the light intensity on a...Ch. 17 - Your friend has been given a laser for her...Ch. 17 - A double slit is illuminated simultaneously with...Ch. 17 - Figure P17.42 shows the light intensity on a...Ch. 17 - A laser beam of wavelength 670 nm shines through a...Ch. 17 - The two most prominent wavelengths in the light...Ch. 17 - A diffraction grating produces a first-order...Ch. 17 - A diffraction grating is illuminated...Ch. 17 - White light (400-700 nm) is incident on a 600...Ch. 17 - A miniature spectrometer used for chemical...Ch. 17 - Figure P17.49 shows the interference pattern on a...Ch. 17 - Figure P17.4919 shows the interference pattern on...Ch. 17 - Because sound is a wave, it is possible to make a...Ch. 17 - The shiny surface of a CD is imprinted with...Ch. 17 - If sunlight shines straight onto a peacock...Ch. 17 - The wings of some beetles have closely spaced...Ch. 17 - A diffraction grating having 500 lines/mm...Ch. 17 - Light emitted by element X passes through a...Ch. 17 - Light of a single wavelength is incident on a...Ch. 17 - A sheet of glass is coated with a 500-nm-thick...Ch. 17 - A soap bubble is essentially a thin film of water...Ch. 17 - A laboratory dish, 20 cm in diameter, is half...Ch. 17 - You need to use your cell phone, which broadcasts...Ch. 17 - Light from a sodium lamp ( = 589 nm) illuminates a...Ch. 17 - The opening to a cave is a tall, 30-cm-wide crack....Ch. 17 - A diffraction grating has 500 slits/mm. What is...Ch. 17 - Figure P17.65 shows the light intensity on a...Ch. 17 - Figure P17.65 shows the light intensity on a...Ch. 17 - Figure P17.67 shows the light intensity on a...Ch. 17 - One day, after pulling down your window shade, you...Ch. 17 - Prob. 70GPCh. 17 - A helium-neon laser ( = 633 nm), shown in Figure...Ch. 17 - In the laser range-finding experiments of Example...Ch. 17 - Prob. 73MSPPCh. 17 - Prob. 74MSPPCh. 17 - Prob. 75MSPP
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