Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 32, Problem 30P
To determine
The distance at which the mirror should be placed from the wall so that a real mage of the object is formed on the wall.
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Sketch the harmonic on graphing paper.
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Sketch the harmonic.
Chapter 32 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 32.1 - Does the result of Example 322 depend on your...Ch. 32.1 - Return to the Chapter-Opening Question, page 837,...Ch. 32.1 - Suppose you are standing about 3 m in front of a...Ch. 32.5 - Light passes from a medium with n = 1.3 into a...Ch. 32.7 - Fill a sink with water. Place a waterproof watch...Ch. 32.7 - It 45.0 plastic lenses are used in binoculars,...Ch. 32 - What would be the appearance of the Moon if it had...Ch. 32 - Archimedes is said to have burned the whole Roman...Ch. 32 - What is the focal length of a plane mirror? What...Ch. 32 - An object is placed along the principal axis of a...
Ch. 32 - Using the rules for the three rays discussed with...Ch. 32 - Prob. 6QCh. 32 - If a concave mirror produces a real image, is the...Ch. 32 - Prob. 8QCh. 32 - When you look at the Moons reflection from a...Ch. 32 - How can a spherical mirror have a negative object...Ch. 32 - Prob. 11QCh. 32 - When you look down into a swimming pool or a lake,...Ch. 32 - Draw a ray diagram to show why a stick looks bent...Ch. 32 - Prob. 14QCh. 32 - You look into an aquarium and view a fish inside....Ch. 32 - Prob. 16QCh. 32 - A ray of light is refracted through three...Ch. 32 - Can a light ray traveling in air be totally...Ch. 32 - When you look up at an object in air from beneath...Ch. 32 - What type of mirror is shown in Fig. 3244?Ch. 32 - Light rays from stars (including our Sun) always...Ch. 32 - (I) When you look at yourself in a 60-cm-tall...Ch. 32 - (I) Suppose that you want to take a photograph of...Ch. 32 - (II) Two plane mirrors meet at a 135 angle, Fig....Ch. 32 - (II) A person whose eyes are 1.64 m above the...Ch. 32 - (II) Show that if two plane mirrors meet at an...Ch. 32 - (II) Suppose you are 88 cm from a plane mirror....Ch. 32 - (II) Stand up two plane minors so they form a 90.0...Ch. 32 - (III) Suppose a third mirror is placed beneath the...Ch. 32 - (I) A solar cooker, really a concave mirror...Ch. 32 - (I) How far from a concave mirror (radius 24.0cm)...Ch. 32 - (I) When walking toward a concave mirror you...Ch. 32 - (II) A small candle is 35 cm from a concave mirror...Ch. 32 - (II) You look at yourself in a shiny...Ch. 32 - (II) A mirror at an amusement park shows an...Ch. 32 - (II) A dentist wants a small mirror that, when...Ch. 32 - (II) Some rearview mirrors produce images of cars...Ch. 32 - (II) You are standing 3.0 m from a convex security...Ch. 32 - (II) An object 3.0 mm high is placed 18 cm from a...Ch. 32 - (II) The image of a distant tree is virtual and...Ch. 32 - (II) Use two techniques, (a) a ray diagram, and...Ch. 32 - (II) Show, using a ray diagram, that the...Ch. 32 - (II) Use ray diagrams to show that the mirror...Ch. 32 - (II) The magnification of a convex mirror is +0.55...Ch. 32 - (II) (a) Where should an object be placed in front...Ch. 32 - (II) A 4.5-cm tall object is placed 26 cm in front...Ch. 32 - (II) A shaving or makeup mirror is designed to...Ch. 32 - (II) Let the focal length of a convex mirror be...Ch. 32 - (II) A spherical mirror of focal length f produces...Ch. 32 - Prob. 30PCh. 32 - (III) A short thin object (like a short length of...Ch. 32 - (I) The speed of light in ice is 2.29 108 m/s....Ch. 32 - (I) What is the speed of light in (a) ethyl...Ch. 32 - (I) Our nearest star (other than the Sun) is 4.2...Ch. 32 - (I) How long does it take light to reach us from...Ch. 32 - (II) The speed of light in a certain substance is...Ch. 32 - (II) Light is emitted from an ordinary lightbulb...Ch. 32 - (I) A diver shines a flashlight upward from...Ch. 32 - (I) A flashlight beam strikes the surface of a...Ch. 32 - Prob. 40PCh. 32 - (I) A light beam coming from an underwater...Ch. 32 - (II) A beam of light in air strikes a slab of...Ch. 32 - (II) A light beam strikes a 2.0-cm-thick piece of...Ch. 32 - (II) An aquarium filled with water has flat glass...Ch. 32 - (II) In searching the bottom of a pool at night, a...Ch. 32 - (II) The block of glass (n = 1.5) shown in cross...Ch. 32 - (II) A laser beam of diameter d1 = 3.0 mm in air...Ch. 32 - (II) Light is incident on an equilateral glass...Ch. 32 - (II) A triangular prism made of crown glass (n =...Ch. 32 - (II) Show in general that for a light beam...Ch. 32 - (III) A light ray is incident on a flat piece of...Ch. 32 - (I) By what percent is the speed of blue light...Ch. 32 - (I) A light beam strikes a piece of glass at a...Ch. 32 - (II) A parallel beam of light containing two...Ch. 32 - (III) A ray of light with wavelength is incident...Ch. 32 - (III) For visible light, the index of refraction n...Ch. 32 - (I) What is the critical angle for the interlace...Ch. 32 - (I) The critical angle for a certain liquidair...Ch. 32 - (II) A beam of light is emitted in a pool of water...Ch. 32 - (II) A ray of light, after entering a light fiber,...Ch. 32 - (II) A beam of light is emitted 8.0cm beneath the...Ch. 32 - (II) Figure 3257 shows a liquid-detecting prism...Ch. 32 - (II) Two rays A and B travel down a cylindrical...Ch. 32 - (II) (a) What is the minimum index of refraction...Ch. 32 - (III) Suppose a ray strikes the left face of the...Ch. 32 - (III) A beam of light enters the end of an optic...Ch. 32 - (II) A 13.0-cm-thick plane piece of glass (n =...Ch. 32 - (II) A fish is swimming in water inside a thin...Ch. 32 - (III) In Section 32-8, we derived Eq. 32-8 for a...Ch. 32 - Two identical concave mirrors are set facing each...Ch. 32 - A slab of thickness D, whose two faces are...Ch. 32 - Two plane mirrors are facing each other 2.2 m...Ch. 32 - We wish to determine the depth of a swimming pool...Ch. 32 - A 1.80-m-tall person stands 3.80 m from a convex...Ch. 32 - Prob. 76GPCh. 32 - Each student in a physics lab is assigned to find...Ch. 32 - A kaleidoscope makes symmetric patterns with two...Ch. 32 - When light passes through a prism, the angle that...Ch. 32 - If the apex angle of a prism is = 72 (see Fig....Ch. 32 - Fermats principle slates that light travels...Ch. 32 - Suppose Fig. 3236 shows a cylindrical rod whose...Ch. 32 - An optical fiber is a long transparent cylinder of...Ch. 32 - An object is placed 15 cm from a certain mirror....Ch. 32 - The end faces of a cylindrical glass rod (n =...Ch. 32 - The paint used or highway signs often contains...
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