Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
bartleby

Concept explainers

Question
Book Icon
Chapter 35, Problem 35.40P
To determine

The angular spread of visible light passing through a prism.

Expert Solution & Answer
Check Mark

Answer to Problem 35.40P

The angular spread of visible light passing through a prism is sin1[nVsin(ϕsin1(sinθnV))]sin1[nRsin(ϕsin1(sinθnR))] .

Explanation of Solution

Given Info:

Explanation:

Write the expression for snell’s law for prism to calculate angle of refraction for red light.

n1sinθ1=n2sin(ϕθ2)sin(ϕθ2)=(n1sinθ1n2)θ2=ϕsin1(n1sinθ1n2) (1)

Here,

n1 is refractive index for air.

θ1 is angle of incidence for red light.

n2 is refractive index for red light.

θ2 is the angle of refraction for red light.

ϕ is the apex angle.

Substitute 1 for n1 , θ for θ1 and nR for n2 in above equation

θ2=ϕsin1(1sinθnR)=ϕsin1(sinθnR)

Write the expression for snell’s law,

n1sinθ1=n2sin(θ2)sin(θ1)=(n2sinθ2n1)θ1=sin1(n2sinθ2n1)

Here,

θ1 is deviation of red light from incidence light.

θ2 is angle of refraction for red light

n1 is the refractive index for air.

n2 is refractive index for red light

Substitute θ2=ϕsin1(sinθnR) for θ2 , 1 for n1 , θR for θ1 and for nR for n2 in above equation.

θR=sin1(nRsin(ϕsin1(sinθnR))1)=sin1(nRsin(ϕsin1(sinθnR)))

Write the expression for snell’s law for prism to calculate angle of refraction for violet light.

n1sinθ1=n2sin(ϕθ2)sin(ϕθ2)=(n1sinθ1n2)θ2=ϕsin1(n1sinθ1n2) (2)

Here,

n1 is refractive index for air.

θ1 is angle of incidence for violet light.

n2 is refractive index for violet light.

θ2 is the angle of refraction for violet light.

ϕ is the apex angle.

Substitute 1 for n1 , θ for θ1 and nV for n2 in equation (2).

θ2=ϕsin1(1sinθnV)=ϕsin1(sinθnV)

Write the expression for Snell's law.

n1sinθ1=n2sin(θ2)sin(θ1)=(n2sinθ2n1)θ1=sin1(n2sinθ2n1)

Here,

θ1 is deviation of violet light from incidence light.

θ2 is angle of refraction for violet light

n1 is the refractive index for air.

n2 is refractive index for violet light.

Substitute θ2=ϕsin1(sinθnV) for θ2 , 1 for n1 , θV for θ1 and for nV for n2 in above equation.

θV=sin1(nVsin(ϕsin1(sinθnV))1)=sin1(nVsin(ϕsin1(sinθnV)))

Write the expression for angular spread of visible light,

ω=θVθR

Here,

θV is deviation of violet light from visible light.

θR is the deviation of red light from visible light.

Substitute sin1(nVsin(ϕsin1(sinθnV))) for θV and sin1(nRsin(ϕsin1(sinθnR))) for θR in above equation.

ω=sin1(nVsin(ϕsin1(sinθnV)))sin1(nRsin(ϕsin1(sinθnR)))

Conclusion:

Therefore, the angular spread of visible light passing through a prism is sin1[nVsin(ϕsin1(sinθnV))]sin1[nRsin(ϕsin1(sinθnR))] .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
34. Consider a beam of light from the left entering a prism of apex angle O as shown in Figure P34.34. Two angles of incidence, 0, and 0,, are shown as well as two angles of refraction, 0, and 0,. Show that O = 0, + 0g- 2 %D 2 3°
The critical angle for total internal reflection at a turpentine-air interface is 42.8°. A ray traveling in the liquid has an angle of incidence of 32.0° at the interface. What angle does the refracted ray in air make with the normal? O51.3° O 14.7° O 53.0° O 23.8° here to search L
The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. A) What is the angular spread (in degrees) of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 51.0°? B) What is the angular spread (in degrees) of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 90°?

Chapter 35 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 35 - The index of refraction for water is about 43....Ch. 35 - Prob. 35.7OQCh. 35 - What is the order of magnitude of the time...Ch. 35 - Prob. 35.9OQCh. 35 - Prob. 35.10OQCh. 35 - A light ray navels from vacuum into a slab of...Ch. 35 - Suppose you find experimentally that two colors of...Ch. 35 - Prob. 35.13OQCh. 35 - Which color light refracts the most when entering...Ch. 35 - Prob. 35.15OQCh. 35 - Prob. 35.1CQCh. 35 - Prob. 35.2CQCh. 35 - Prob. 35.3CQCh. 35 - The F-117A stealth fighter (Fig. CQ35.4) is...Ch. 35 - Prob. 35.5CQCh. 35 - Prob. 35.6CQCh. 35 - Prob. 35.7CQCh. 35 - Prob. 35.8CQCh. 35 - A laser beam passing through a non homogeneous...Ch. 35 - Prob. 35.10CQCh. 35 - Prob. 35.11CQCh. 35 - (a) Under what conditions is a mirage formed?...Ch. 35 - Figure CQ35.13 shows a pencil partially immersed...Ch. 35 - Prob. 35.14CQCh. 35 - Prob. 35.15CQCh. 35 - Prob. 35.16CQCh. 35 - Prob. 35.17CQCh. 35 - Prob. 35.1PCh. 35 - The Apollo 11 astronauts set up a panel of...Ch. 35 - Prob. 35.3PCh. 35 - As a result of his observations, Ole Roemer...Ch. 35 - The wavelength of red helium-neon laser light in...Ch. 35 - An underwater scuba diver sees the Sun at an...Ch. 35 - A ray of light is incident on a flat surface of a...Ch. 35 - Figure P35.8 shows a refracted light beam in...Ch. 35 - Prob. 35.9PCh. 35 - A dance hall is built without pillars and with a...Ch. 35 - Prob. 35.11PCh. 35 - A ray of light strikes a flat block of glass (n =...Ch. 35 - A prism that has an apex angle of 50.0 is made of...Ch. 35 - Prob. 35.14PCh. 35 - A light ray initially in water enters a...Ch. 35 - A laser beam is incident at an angle of 30.0 from...Ch. 35 - A ray of light strikes the midpoint of one face of...Ch. 35 - Prob. 35.18PCh. 35 - When you look through a window, by what time...Ch. 35 - Two flat, rectangular mirrors, both perpendicular...Ch. 35 - Prob. 35.21PCh. 35 - Prob. 35.22PCh. 35 - Two light pulses are emitted simultaneously from a...Ch. 35 - Light passes from air into flint glass at a...Ch. 35 - A laser beam with vacuum wavelength 632.8 nm is...Ch. 35 - A narrow beam of ultrasonic waves reflects off the...Ch. 35 - Prob. 35.27PCh. 35 - A triangular glass prism with apex angle 60.0 has...Ch. 35 - Light of wavelength 700 nm is incident on the face...Ch. 35 - Prob. 35.30PCh. 35 - Prob. 35.31PCh. 35 - Prob. 35.32PCh. 35 - Prob. 35.33PCh. 35 - A submarine is 300 m horizontally from the shore...Ch. 35 - Prob. 35.35PCh. 35 - The index of refraction for red light in water is...Ch. 35 - A light beam containing red and violet wavelengths...Ch. 35 - The speed of a water wave is described by v=gd,...Ch. 35 - Prob. 35.39PCh. 35 - Prob. 35.40PCh. 35 - A glass optical fiber (n = 1.50) is submerged in...Ch. 35 - For 589-nm light, calculate the critical angle for...Ch. 35 - Prob. 35.43PCh. 35 - A triangular glass prism with apex angle has an...Ch. 35 - Prob. 35.45PCh. 35 - Prob. 35.46PCh. 35 - Consider a common mirage formed by superheated air...Ch. 35 - A room contains air in which the speed of sound is...Ch. 35 - An optical fiber has an index of refraction n and...Ch. 35 - Prob. 35.50PCh. 35 - Prob. 35.51APCh. 35 - Consider a horizontal interface between air above...Ch. 35 - Prob. 35.53APCh. 35 - Why is the following situation impossible? While...Ch. 35 - Prob. 35.55APCh. 35 - How many times will the incident beam in Figure...Ch. 35 - When light is incident normally on the interface...Ch. 35 - Refer to Problem 37 for its description of the...Ch. 35 - A light ray enters the atmosphere of the Earth and...Ch. 35 - A light ray enters the atmosphere of a planet and...Ch. 35 - Prob. 35.61APCh. 35 - Prob. 35.62APCh. 35 - Prob. 35.63APCh. 35 - Prob. 35.64APCh. 35 - The light beam in Figure P35.65 strikes surface 2...Ch. 35 - Prob. 35.66APCh. 35 - A 4.00-m-long pole stands vertically in a...Ch. 35 - Prob. 35.68APCh. 35 - A 4.00-m-long pole stands vertically in a...Ch. 35 - As sunlight enters the Earths atmosphere, it...Ch. 35 - Prob. 35.71APCh. 35 - A ray of light passes from air into water. For its...Ch. 35 - As shown in Figure P35.73, a light ray is incident...Ch. 35 - Prob. 35.74APCh. 35 - Prob. 35.75APCh. 35 - Prob. 35.76APCh. 35 - Prob. 35.77APCh. 35 - Students allow a narrow beam of laser light to...Ch. 35 - Prob. 35.79APCh. 35 - Figure P34.50 shows a top view of a square...Ch. 35 - Prob. 35.81CPCh. 35 - Prob. 35.82CPCh. 35 - Prob. 35.83CPCh. 35 - Pierre de Fermat (16011665) showed that whenever...Ch. 35 - Prob. 35.85CPCh. 35 - Suppose a luminous sphere of radius R1 (such as...Ch. 35 - Prob. 35.87CP
Knowledge Booster
Background pattern image
Physics
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning