Concept explainers
(a)
The time at which the light arrives at
(a)
Answer to Problem 84CP
The time at which the light arrives at
Explanation of Solution
Write the expression to obtain the
Here,
Write the expression to obtain the speed of light in medium
Here,
Write the expression to obtain the time when light arrive at point
Here,
Substitute
The light ray path in two mediums is as shown in the figure below.
Figure-(1)
Write the expression to obtain the value of
Here,
Write the expression to obtain the value of
Here,
Substitute
Therefore, the time at which the light arrives at
(b)
The result is
(b)
Answer to Problem 84CP
The result is
Explanation of Solution
Consider the equation (II).
Differentiate the above equation with respect to
Substitute
Therefore, the result is
(c)
The expression of Snell’s law is given as
(c)
Answer to Problem 84CP
The expression of Snell’s law is given as
Explanation of Solution
Write the expression to obtain the value of
Write the expression to obtain the value of
Substitute
Therefore, the expression of Snell’s law is given as
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Chapter 35 Solutions
Physics for Scientists and Engineers With Modern Physics
- An incident light ray is aimed at the open top of a tank filled with Benzene, kerosene and glycerin. Determine the angle of incidence and refraction of the light at the 1st and 3rd mediums if the angle in the 2nd medium is 20°. The indices of refraction for kerosene and glycerin are 1.39 and 1.46 respectively. What is the index of refraction of the first medium if the light ray travels the first medium at is 2 x 10^8 m/s.arrow_forwardA beam of light traveling through a liquid (of index of refraction n1 = 1.51) is incident on a surface at an angle of θ1 = 59° with respect to the normal to the surface. It passes into the second medium and refracts at an angle of θ2 = 69° with respect to the normal. a) What is the index of refraction of the second material? b) Numerically, what is the light's velocity in medium 1, in meters per second? c) Numerically, what is the light's velocity in medium 2, in meters per second?arrow_forwardAs sunlight enters the Earth’s atmosphere, it changes direction due to the small difference between the speeds of light in vacuum and in air. The duration of an optical day is defined as the time interval between the instant when the top of the rising Sun is just visible above the horizon andthe instant when the top of the Sun just disappears below the horizontal plane. The duration of the geometric day is defined as the time interval between the instant a mathematically straight line between an observer and the top of the Sun just clears the horizon and the instant this linejust dips below the horizon. (a) Explain which is longer, an optical day or a geometric day. (b) Find the difference between these two time intervals. Model the Earth’s atmosphere as uniform, with index of refraction 1.000 293, a sharply defined upper surface, and depth 8 614 m. Assume the observer is at the Earth’s equator so that the apparent path of the rising and setting Sun is perpendicular to the horizon.arrow_forward
- The drawing illustrates the dispersion of light by a prism. The prism is made from a certain type of glass, and has a cross section shaped like an equilateral triangle. The indices of refraction for the red and violet light in this type of glass are 1.608 and 1.639, respectively. The angle of incidence for both the red and violet light is 60.0°. Find the angles of refraction at which the (a) red and (b) violet rays emerge into the air from the prism.arrow_forwardA beam of light traveling in air strikes a slab of transparent material. The incident beam makes an angle of 60° with the normal, and the refracted beam make an angle of 50° with the normal. What is the speed of light in the transparent material? (c = 3.0 × 108 m/s) Provide the answer: x 108 m/sarrow_forwardWhen a ray of light changes media , it will refract (bend). With angles being measured from the normal, the amount of refraction can be found using Snell's Law . Traveling through any medium light will have a speed given by the equation shown where n represents the index of refraction and is the speed of light in a vacuum (3 * 10 ^ 8 * m/c) . A) In the picture of refraction shown which index of refraction is larger n1 or n2 B)In what medium does the lightbeam shown travel faster C) Measure the angles, Assuming n1 refers to vaccum what is the value of n2? How fast does light travel within n2?arrow_forward
- Consider the following situation for the next two problems. A piece of transparent material with unknown index of refraction is immersed in water (n = 1.333). A ray of light propagating within the material strikes the top surface at an angle of 0, = 58° as shown below and undergoes total internal reflection. This is the smallest incident angle for which total internal reflection can occur. The reflected ray then hits the right side of the material and enters the surrounding water at an angle of 0,. Note: Figure not to scale. water 0f 2-15 What is the index of refraction of the transparent material? (± 0.002)arrow_forwardA beam of light traveling through a liquid (of index of refraction n1 = 1.3) is incident on a surface at an angle of θ1 = 55° with respect to the normal to the surface. It passes into the second medium and refracts at an angle of θ2 = 65° with respect to the normal. Part (a) Write an equation for the index of refraction of the second material. Part (b) What is the index of refraction of the second material? Part (c) Numerically, what is the light's velocity in medium 1, in meters per second? Part (d) Numerically, what is the light's velocity in medium 2, in meters per second?arrow_forwardThe drawing shows a ray of light traveling from point A to point B, a distance of 9.10 m in a material than has an index of refraction n₁. At point B, the light encounters a different substance whose index of refraction is n₂ = 1.63. The light strikes the interface at the critical angle of 0c = 58.9°. How much time does it take for the light to travel from A to B? Number i n₂ = 1.63 n1 A Units >arrow_forward
- Consider a layer of Oil, Glass, and Air where the oil/glass boundary is parallel to the glass/air boundary. Let the index of refraction for the glass be 1.55 and the index of refraction for the oil to be 1.31. At what angle relative to the normal should a ray of light be directed upon the oil/glass interface such that it strikes the glass/air interface at the critical angle?arrow_forwardProblem 2: A beam of light traveling through a liquid (of index of refraction n1 = 1.31) is incident on a surface at an angle of θ1 = 55° with respect to the normal to the surface. It passes into the second medium and refracts at an angle of θ2 = 66.5° with respect to the normal. Part (a) Write an equation for the index of refraction of the second material. Part (b) What is the index of refraction of the second material? Part (c) Numerically, what is the light's velocity in medium 1, in meters per second? Part (d) Numerically, what is the light's velocity in medium 2, in meters per second?arrow_forwardConsider a ray of light that propagates from air ( n=1 ) to any one of the materials listed below. Assuming that the ray strikes the interface with any of the listed materials always at the same angle θ1 , in which material will the direction of propagation of the ray change the most due to refraction? What is the critical angle θcrit for light propagating from a material with index of refraction of 1.50 to a material with index of refraction of 1.00?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning