Explanation Given info: The refractive index of the material is n . Τhe radius of the curvature of the material is R . The light parallel to the base of the material strikes it from a height L . The emergent ray makes an angle θ with the material. Let the angle of incidence is γ as shown in figure below. Figure (I) From the Figure (1) from triangle O P Q , sin γ = L R γ = sin − 1 ( L R ) From the Figure (1) from triangle O P Q , cos γ = ( R 2 − L 2 ) R From Snell’s Law n 1 sin γ = n 2 sin ϕ (1) Here, n 1 is the refractive index of the vacuum. n 2 is the refractive index of material. γ is the angle of incidence. ϕ is the angle of refraction at point P. Substitute 1.00 for n 1 , n for n 2 in equation (1). ( 1.00 ) sin γ = n sin ϕ sin ϕ = sin γ n Substitute L R for sin γ in the above equation. sin ϕ = L n R ϕ = sin − 1 ( L n R ) The value of cos ϕ is , cos ϕ = 1 − sin 2 ϕ Substitute L n R for sin ϕ in the above equation. cos ϕ = n 2 R 2 − L 2 n R From figure (1) in triangle OPS , ϕ + ( α + 90.0 ° ) + ( 90.0 ° − γ ) = 180 α = γ − ϕ Apply Snell’s law at the point S. n 2 sin θ = n 1 sin α Here, n 2 is the refractive index of vacuum. n 1 is the refractive index of the material. Substitute 1.00 for n 2 , n for n 1 , γ − ϕ for α in the above equation. 1.00 sin θ = n sin ( γ − ϕ ) sin θ = n sin ( γ − ϕ ) (2) From trigonometry, the formula of sin ( γ − ϕ ) is, sin ( γ − ϕ ) = sin γ cos ϕ − cos γ sin ϕ Substitute sin γ cos ϕ − cos γ sin ϕ for sin ( γ − ϕ ) in equation (2). sin θ = n ( sin γ cos ϕ − cos γ sin ϕ ) Substitute L R for sin γ , ( R 2 − L 2 ) R for cos γ , L n R for sin ϕ n 2 R 2 − L 2 n R for cos ϕ in the above equation

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN: 9781337553292

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Dispersion of White Light

Snell’s law is a formula that gives a relation between the angle of incidence and angle of refraction and is given as:

Question

Chapter 34, Problem 43AP

To determine

The relation between the emergent angle and n , R and L .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 34, Problem 42AP

Chapter 34, Problem 44AP

Students have asked these similar questions

A light ray traveling in air is incident on one face of a right-angle prism with index of refraction n = 1.49, as shown in Figure P22.54, and the ray follows the path shown in the figure. Assuming that θ = 58.0° and the base of the prism is mirrored, determine the angle made by the outgoing ray with the normal to the right face of the prism.?degrees

A light ray in the core (n 1.40) of a cylindrical optical fiber travels at an angle Θ1 = 49.0° with respect to the axis of the fiber. A ray is transmitted through the cladding (n 1.20) and into the air. What angle Θ2 does the exiting ray make withthe outside surface of the cladding

A ray of light strikes a flat glass block at an incidence angle of ?1 = 34.4°. The glass is 2.00 cm thick and has an index of refraction that equals ng = 1.20. A light ray incident on a glass block of thickness 2.00 cm is shown. The ray travels down and to the right and is incident to the top of the block at an angle ?1 to the normal of the surface. The ray inside the block moves down and to the right but at a steeper slope than the incident ray, making an angle of ?2 with the vertical. It is incident on the bottom surface of the block, making an angle of ?3 with the vertical, and exits moving down and to the right, at a less steep slope, making an angle of ?4 with the vertical. A dashed line extends from the original path of the ray down in the block and is shown to be a distance d from the ray that exits the glass block. d) The distance d separates the twice-bent ray from the path it would have taken without the glass in the way. What is this distance (in cm)? cm (e) At…

Chapter 34 Solutions

Physics for Scientists and Engineers with Modern Physics

Ch. 34.3 - Prob. 34.1QQ Ch. 34.4 - If beam is the incoming beam in Figure 34.10b,...Ch. 34.4 - Light passes from a material with index of...Ch. 34.6 - Prob. 34.4QQ Ch. 34.7 - Prob. 34.5QQ Ch. 34 - In an experiment to measure the speed of light...Ch. 34 - Prob. 2P Ch. 34 - As a result of his observations, Ole Roemer...Ch. 34 - Prob. 4P Ch. 34 - You are working for an optical research company...

Ch. 34 - Prob. 6P Ch. 34 - Prob. 7P Ch. 34 - Prob. 8P Ch. 34 - Prob. 9P Ch. 34 - A ray of light strikes a flat block of glass (n =...Ch. 34 - Prob. 11P Ch. 34 - Prob. 12P Ch. 34 - Prob. 13P Ch. 34 - Prob. 14P Ch. 34 - When you look through a window, by what time...Ch. 34 - Prob. 16P Ch. 34 - You have just installed a new bathroom in your...Ch. 34 - Prob. 18P Ch. 34 - Prob. 19P Ch. 34 - Prob. 20P Ch. 34 - Prob. 21P Ch. 34 - A submarine is 300 m horizontally from the shore...Ch. 34 - Prob. 23P Ch. 34 - Prob. 24P Ch. 34 - Prob. 25P Ch. 34 - Prob. 26P Ch. 34 - Prob. 27P Ch. 34 - Prob. 28P Ch. 34 - Prob. 29P Ch. 34 - Prob. 30P Ch. 34 - An optical fiber has an index of refraction n and...Ch. 34 - Prob. 32AP Ch. 34 - How many times will the incident beam in Figure...Ch. 34 - Prob. 34AP Ch. 34 - Prob. 35AP Ch. 34 - Prob. 36AP Ch. 34 - Prob. 37AP Ch. 34 - Prob. 38AP Ch. 34 - Prob. 39AP Ch. 34 - A light ray enters the atmosphere of a planet and...Ch. 34 - Prob. 41AP Ch. 34 - Prob. 42AP Ch. 34 - Prob. 43AP Ch. 34 - Prob. 44AP Ch. 34 - Prob. 45AP Ch. 34 - Prob. 46AP Ch. 34 - Prob. 47AP Ch. 34 - Prob. 48AP Ch. 34 - Prob. 49AP Ch. 34 - Figure P34.50 shows a top view of a square...Ch. 34 - Prob. 51AP Ch. 34 - Prob. 52CP Ch. 34 - Prob. 53CP Ch. 34 - Pierre de Fermat (16011665) showed that whenever...Ch. 34 - Prob. 55CP Ch. 34 - Prob. 56CP Ch. 34 - Prob. 57CP

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.