COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 23, Problem 85QAP
To determine

The speed of light and refractive index of different optical materials

Expert Solution & Answer
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Answer to Problem 85QAP

The completed table is shown below.

    Optical material with percentage of time required for light to pass through compared to an equal length of vacuumSpeed of light(meter/sec)Index of refraction
    100%  3×1081
    125%  2.4×1081.25
    150%  2×1081.5
    200%  1.5×1082
    500%  6×1075
    1000%  3×10710

Explanation of Solution

Given info:

The given table is shown below,

    Optical material with percentage of time required for light to pass through compared to an equal length of vacuumSpeed of light(meter/sec)Index of refraction
    100%
    125%
    150%
    200%
    500%
    1000%

Formula used:

The speed of light in a given optical material can be expressed as the ratio of the time that is required for light to travel through a length of vacuum to the time required for light to travel through the same length of the optical material.

Time required for light to travel through a length of vacuum = tvacuum

Time required for light to travel through the same length of optical material = tmedium

The ratio of time is, r =tvacuumtmedium

The velocity of light in the optical medium is,

  v =vvac×(t vacuumt medium) = (3×108)×(t vacuumt medium)m/s

Refractive index of an optical material is calculated by using the following relation

  n= vvacv=3×108 m/sv

Calculation:

For 100%,

  r =tvacuumtmedium=tvacuum100100×tvacuum=11=1

Similarly,

The ratio is calculated for different percentage as shown below.

    Optical material with percentage of time required for light to pass through compared to an equal length of vacuumtmedium=%oftvacuumr =tvacuumtmedium
    100%11
    125%1.250.8
    150%1.50.67
    200%20.5
    500%50.2
    1000%100.1

Now, the velocity of light in a material is,

  v =vvac×(t vacuumt medium) = (3×108)×(t vacuumt medium)m/s

The refractive index is,

  n= vvacv=3×108 m/sv

So, for 100%,

  v = r×(3×108)m/s=1×3×108m/s=3×108m/s

  n=3×108 m/s3×108m/s=1

Similarly, the speed as well as refractive index for different percentage is shown below.

    Optical material with percentage of time required for light to pass through compared to an equal length of vacuumSpeed of light(meter/sec)Index of refraction
    100%  3×1081
    125%  2.4×1081.25
    150%  2×1081.5
    200%  1.5×1082
    500%  6×1075
    1000%  3×10710

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Chapter 23 Solutions

COLLEGE PHYSICS

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