Explanation Figure below represents the geometry of the given situation. Let P is the person and L is the light bulb. According to the law of reflection the angle on either side of the dashed line at O are equal. From the triangle O P C , write the expression for cos θ . cos θ = d l 1 (I) Here, θ is the angle, d is the perpendicular distance of a person from the mirror, and l 1 is the distance travelled by the light between the mirror and person. Solve equation (I) for l 1 . l 1 = d cos θ (II) From the triangle O P C , write the expression for sin θ . sin θ = x 1 l 1 (III) Here, x 1 is the shortest distance between the mirror and person. Solve equation (III) for x 1 . x 1 = l 1 sin θ (IV) From the triangle O L B , write the expression for cos θ . cos θ = 2 d l 2 (V) Here, l 2 is the distance travelled by the light between the mirror and bulb. Solve equation (V) for l 2 . l 2 = 2 d cos θ (VI) From the triangle O L B , write the expression for sin θ . sin θ = x 2 l 2 (VII) Here, x 2 is the shortest distance between the mirror and bulb. Solve equation (VII) for x 2 . x 2 = l 2 sin θ (VIII) In the problem, the condition given that the total distance travelled by the light when it travels to the mirror and reflects from the mirror to the person is 3.10 times the distance travelled by the light when it travels directly to the person without reflecting off the mirror. That is n = 3.10 . This condition can be expressed as, l 1 + l 2 = n l (IX) Here, l is the shortest distance between the person and bulb. Use equation (II) and (VI) in (IX). d cos θ + 2 d cos θ = n l 3 d cos θ = n l (X) Apply Pythagorean theorem in the triangle A P L

Principles of Physics: A Calculus-Based Text

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Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Ch. 25.3 - Prob. 25.1QQ Ch. 25.4 - If beam is the incoming beam in Active Figure...Ch. 25.4 - Light passes from a material with index of...Ch. 25.4 - Prob. 25.4QQ Ch. 25.5 - Prob. 25.5QQ Ch. 25.7 - Prob. 25.6QQ Ch. 25.7 - Prob. 25.7QQ Ch. 25 - Prob. 1OQ Ch. 25 - Prob. 2OQ Ch. 25 - What happens to a light wave when it travels from...

Ch. 25 - Prob. 4OQ Ch. 25 - The index of refraction for water is about 43....Ch. 25 - Prob. 6OQ Ch. 25 - Light traveling in a medium of index of refraction...Ch. 25 - Prob. 8OQ Ch. 25 - The core of an optical fiber transmits light with...Ch. 25 - Prob. 10OQ Ch. 25 - A light ray travels from vacuum into a slab of...Ch. 25 - Prob. 12OQ Ch. 25 - Prob. 13OQ Ch. 25 - Prob. 14OQ Ch. 25 - Prob. 1CQ Ch. 25 - Prob. 2CQ Ch. 25 - Prob. 3CQ Ch. 25 - Prob. 4CQ Ch. 25 - Prob. 5CQ Ch. 25 - Prob. 6CQ Ch. 25 - Prob. 7CQ Ch. 25 - Prob. 8CQ Ch. 25 - Prob. 9CQ Ch. 25 - Prob. 10CQ Ch. 25 - Prob. 11CQ Ch. 25 - Prob. 12CQ Ch. 25 - Prob. 1P Ch. 25 - Prob. 2P Ch. 25 - Prob. 3P Ch. 25 - Prob. 4P Ch. 25 - Prob. 5P Ch. 25 - Prob. 6P Ch. 25 - Prob. 7P Ch. 25 - An underwater scuba diver sees the Sun at an...Ch. 25 - Prob. 9P Ch. 25 - Prob. 10P Ch. 25 - A ray of light is incident on a flat surface of a...Ch. 25 - A laser beam is incident at an angle of 30.0 from...Ch. 25 - Prob. 13P Ch. 25 - A light ray initially in water enters a...Ch. 25 - Find the speed of light in (a) flint glass, (b)...Ch. 25 - Prob. 16P Ch. 25 - Prob. 17P Ch. 25 - Prob. 18P Ch. 25 - Unpolarized light in vacuum is incident onto a...Ch. 25 - Prob. 20P Ch. 25 - Prob. 21P Ch. 25 - Prob. 22P Ch. 25 - Prob. 23P Ch. 25 - Prob. 24P Ch. 25 - 14. A ray of light strikes the midpoint of one...Ch. 25 - Prob. 26P Ch. 25 - Prob. 27P Ch. 25 - Prob. 28P Ch. 25 - Prob. 29P Ch. 25 - Prob. 30P Ch. 25 - Prob. 31P Ch. 25 - Around 1965, engineers at the Toro Company...Ch. 25 - Prob. 33P Ch. 25 - Prob. 34P Ch. 25 - Prob. 35P Ch. 25 - Prob. 36P Ch. 25 - Prob. 37P Ch. 25 - Prob. 38P Ch. 25 - Prob. 39P Ch. 25 - Prob. 40P Ch. 25 - Prob. 41P Ch. 25 - Prob. 42P Ch. 25 - A 4.00-m-long pole stands vertically in a...Ch. 25 - Prob. 44P Ch. 25 - Prob. 45P Ch. 25 - Prob. 46P Ch. 25 - Prob. 47P Ch. 25 - Prob. 48P Ch. 25 - When light is incident normally on the interface...Ch. 25 - Prob. 50P Ch. 25 - Prob. 51P Ch. 25 - Prob. 52P Ch. 25 - The light beam in Figure P25.53 strikes surface 2...Ch. 25 - Prob. 54P Ch. 25 - Prob. 55P Ch. 25 - Prob. 56P Ch. 25 - Prob. 57P Ch. 25 - Prob. 58P Ch. 25 - Prob. 59P Ch. 25 - Prob. 60P Ch. 25 - Prob. 61P Ch. 25 - Prob. 62P

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