Review  Session  1 Dr. Flera Rizatdinova

Summary of Chapter 22 •  Electromagnetic waves are produced by accelerating charges; the

propagation speed is given by:

•  The fields are perpendicular to each other and to the direction of propagation.

•  The wavelength and frequency of EM waves are related:

•  The electromagnetic spectrum includes all wavelengths, from radio waves through visible light to gamma rays.

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Ch. 22 Energy in EM Waves Energy is stored in both electric and magnetic fields, giving the total energy density of an electromagnetic wave:

Each field contributes half the total energy density.

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(22-5)

(22-6a)

Ch. 22 Energy in EM Waves The energy transported through a unit area per unit time is called the intensity:

Its average value is given by:

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(22-7)

(22-8)

Question •  Which of the following statements about

electromagnetic waves in free space are true? (There could be more than one correct choice.)

A) The higher-frequency travel faster than the lower-frequency waves. B) The higher-frequency waves have shorter wavelengths than the lower-frequency waves. C) The wavelengths of the visible waves are some of the longest electromagnetic waves. D) The wavelengths of the visible waves are some of the shortest electromagnetic waves. E) The electric field vector is always at right angles to the magnetic field vector. •  Answer: B, E

Summary of Chapter 23 •  Index of refraction:

•  Angle of reflection equals angle of incidence

•  Plane mirror: image is virtual, upright, and the same size as the object

•  Spherical mirror can be concave or convex

•  Focal length of the mirror:

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Summary of Chapter 23 •  Mirror equation:

•  Magnification:

•  Real image: light passes through it

•  Virtual image: light does not pass through

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Summary of Chapter 23 •  Law of refraction (Snell’s law):

•  Total internal reflection occurs when angle of incidence is greater than critical angle:

•  A converging lens focuses incoming parallel rays to a point

•  A diverging lens spreads incoming rays so that they appear to come from a point

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Summary of Chapter 23 •  Power of a lens:

•  Thin lens equation:

•  Magnification:

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MC  Question •  A wrench is placed at 30 cm in front of a diverging

lens with a focal length of magnitude 10 cm. What is the magnification of the wrench?

•  A) 0.25 •  B) -0.25 •  C) 0.67 •  D) -0.67 •  E) 4.0 •  Answer: A

Problem  1 •  A beam of light in air strikes a slab of glass (n = 1.51)

and is partially reflected and partially refracted. Determine the angle of incidence if the angle of reflection is twice the angle of refraction.

•  Answer: 81.9°

Problem  2 •  An object is placed 9.5 cm in front of a convex lens

with a focal length of magnitude 24 cm. •  (a) Where is the image formed and how far is it from

the lens? •  (b) What is the magnification produced by the

lens? •  Answer: (a) 16 cm in front of the lens (b) 1.7

Problem  3 •  A bright object and a viewing screen are separated

by a distance of 86.0 cm. At what location(s) between the object and the screen should a lens of focal length 16.0 cm be placed in order to produce a sharp image on the screen?

•  Answer: do=64.7cm and do =21.3 cm

Summary of Chapter 24 •  Wavelength of light in a medium with index of refraction n:

•  In the double-slit experiment, constructive interference occurs when

•  and destructive interference when

•  Diffraction grating:

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Summary of Chapter 24 •  Light bends around obstacles and openings in its path, yielding

diffraction patterns

•  Light passing through a narrow slit will produce a central bright maximum of width:

•  The intensity of plane polarized light is reduced after it passes through another polarizer:

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MC  Q2 •  Blue light of wavelength λpasses through a single slit of width d and forms a diffraction pattern on a screen. If we replace the blue light by red light of wavelength 2λ, we can retain the original diffraction pattern if we change the slit width

•  (a) to d/4. •  (b) to d/2. •  (c) not at all. •  (d) to 2d. •  (e) to 4d.

•  Answer: D

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Problem  4 •  Light of wavelength 470 nm in air shines on two slits 6.00 × 10–2

mm apart. The slits are immersed in water, as is a viewing screen 40.0 cm away. How far apart are the fringes on the screen?

•  Answer: 2.4 ×10-3 m

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Problem  5 •  When yellow sodium light, λ= 589 nm, falls on a

diffraction grating, its first-order peak on a screen 72.0 cm away falls 3.32 cm from the central peak. Another source produces a line 3.71 cm from the central peak. What is its wavelength? How many slits/cm are on the grating?

•  Answer: 658 nm; 782 lines/cm

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Problem  6 •  Two polarizers are oriented at 48° to each other and

plane-polarized light is incident on them. If only 35% of the light gets through both of them, what was the initial polarization direction of the incident light?

I1 = I0 cos2θ1; I2 = I1cos

2θ2 = I0 cos2θ1cos

2θ2 = 0.35I0 →

θ1 = cos−1 0.35cosθ2

#

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&

'((= cos

−1 0.35cos 48°

#

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&

'((= 28

°

Summary of Chapter 25 •  Simple magnifier: object at focal point

•  Angular modification:

•  Astronomical telescope: objective and eyepiece; object infinitely far away

•  Telescope magnification:

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Summary of Chapter 25 •  Compound microscope magnification:

•  Resolution of optical devices is limited by diffraction

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M =Nfe

!

"#

$

%&l − fedo

!

"#

$

%&

θ =1.22λD

Problem  8 •  A nearsighted person has a far point of 18 cm.

What power contact lenses will allow this person to comfortably see distant objects clearly?

•  A) +5.6 diopters •  B) -5.6 diopters •  C) +0.056 diopters •  D) -0.056 diopters •  Answer: B

Problem  9 •  The objective lens of a microscope has a focal length

of 2.4 mm and the eyepiece has an angular magnification of 15. The object is positioned 0.060 mm beyond the focal point of the objective. The focal point of the eyepiece is positioned at the real image formed by the objective. The near point of the microscope user is at 25 cm. What is the magnitude of the overall magnification of the microscope?

•  Answer: 600