31Velocity of Light

📚
VELOCITY OF LIGHT
▢ Basic Values:

Table 1: Velocity of Light

Medium / Condition
Velocity / Formula
Vacuum / free space
\(c=3\times10^8\ m/s\)
Vacuum formula
\(c=\frac{1}{\sqrt{\epsilon_0\mu_0}}\)
Electromagnetic wave relation
\(c=\frac{E}{B}=3\times10^8\ m/s\)
Medium
\(v=\frac{1}{\sqrt{\epsilon_0\epsilon_r\mu_0\mu_r}}\)
Medium
\(v=\frac{c}{\sqrt{\epsilon_r\mu_r}}\)
Using refractive index
\(v=\frac{c}{\mu}\)
❖ Important Relation: Higher refractive index → lower velocity of light
▢ Optical Media:

Table 1: Isotropic vs Anisotropic Optical Medium

Medium
Velocity of light
Examples
Isotropic optical medium
Same in all directions
Water, air, glass
Anisotropic optical medium
Different in different directions
Crystals like calcite, quartz
▢ Methods of Determination of Velocity of Light:
❖ Fizeau's Method:
◉ Principle: Laboratory method using rotating toothed wheel

Table 1: Fizeau's Method Formulae

Condition
Formula
First eclipse
\(c=4mnd\)
\(p^{th}\) eclipse
\(c=\frac{4mnd}{2p-1}\)

Table 2: Symbols

Symbol
Meaning
\(m\)
Number of teeth of rotating wheel
\(n\)
Number of rotations per second of wheel when first eclipse occurs
\(d\)
Distance between wheel and mirror
\(p\)
Number of eclipses
❖ Foucault's Method:
◉ Use: Measures velocity of light in air and in medium
◉ Importance: Provides evidence in favour of Huygens' wave theory and against Newton's corpuscular theory

Table 1: Foucault's Method Formulae

Formula
Expression
Velocity of light
\(c=\frac{8\pi NR^2a}{(b+R)x}\)
Using mirror rotation angle
\(c=\frac{4\pi NR}{\theta}\)

Table 2: Symbols

Symbol
Meaning
\(R\)
Distance between plane mirror and concave mirror
\(N\)
Number of rotations of rotating mirror per second
\(a\)
Distance of object from achromatic lens
\(b+R\)
Distance of image from achromatic lens
\(x\)
Shift of image
\(\theta\)
Angle turned by mirror
◉ Important Point: Confirmed that light travels more slowly in water than in air
❖ Michelson's Method:
◉ Feature: Most accurate method for determining velocity of light
◉ Instrument: Uses octagonal mirror
◉ Formula: \(c=8nd\)

Table 1: Symbols

Symbol
Meaning
\(n\)
Number of rotations per second of octagonal mirror
\(d\)
Distance travelled by light
▢ Colour and Velocity:

Table 1: Colour, Velocity and Sensitivity

Fact
Answer
Colour of light depends on
Wavelength
All colours in vacuum
Same speed
In medium
Red has maximum speed
In medium
Violet has minimum speed
Photographic plate most sensitive to
Violet light
Photographic plate least sensitive to
Red light
Reason
Red has larger wavelength
▢ Refraction and Light Parameters:

Table 1: Changes During Refraction

Quantity
Change
Velocity
Changes
Wavelength
Changes
Frequency
Remains unchanged
▢ Read and Digest:

Table 1: Important Points

Fact
Answer
Objects visible from all directions
Due to scattering of light
Colour of light
Depends on wavelength
On refraction
Velocity and wavelength change; frequency remains same
Speed of colours in vacuum
All colours have same speed
Speed of colours in medium
Red maximum, violet minimum
Photographic plate sensitivity
Most sensitive to violet, least to red
Light slower in water than air confirmed by
Foucault's method
Most accurate method
Michelson's method
Rectilinear propagation
Light appears to travel in straight line because wavelength is very small
Ray optics valid when
Characteristic dimensions are much larger than wavelength of light
▢ High-Yield Recall:

Table 1: Velocity of Light One-Liners

Fact
Answer
Velocity of light in vacuum
\(3\times10^8\ m/s\)
Vacuum speed formula
\(c=\frac{1}{\sqrt{\epsilon_0\mu_0}}\)
EM wave relation
\(c=\frac{E}{B}\)
Speed in medium
\(v=\frac{c}{\mu}\)
Higher refractive index
Lower velocity of light
Isotropic medium
Velocity same in all directions
Anisotropic medium
Velocity different in different directions
Fizeau's method
Rotating toothed wheel
Fizeau first eclipse
\(c=4mnd\)
Fizeau \(p^{th}\) eclipse
\(c=\frac{4mnd}{2p-1}\)
Foucault's method
Rotating mirror
Foucault evidence
Supports Huygens' wave theory
Foucault confirmed
Light slower in water than air
Michelson's method
Octagonal mirror
Michelson formula
\(c=8nd\)
Most accurate method
Michelson's method
During refraction
Velocity and wavelength change
During refraction
Frequency unchanged
Colour depends on
Wavelength
In vacuum colour speeds
All same
In medium fastest colour
Red
In medium slowest colour
Violet
Photographic plate most sensitive
Violet
Light travels straight because
Wavelength is very small
Ray optics condition
Object/aperture dimensions ≫ wavelength
Q1.
Which method is used to measure the speed of light accurately?
📅BP 2013
Q2.
Velocity of light is equal to
📅BP 2009
Q3.
Time taken by light to cross a glass slab of thickness 5 cm and refractive index 1.5 will be
📅MOE 2013
Q4.
For which color the velocity of light is maximum in diamond?
📅MOE 2011
Q5.
The refractive index of diamond is 2.4, velocity of light in diamond is
📅MOE 2010
Q6.
The correct sequence of electromagnetic waves in decreasing order of frequency:
Q7.
The velocity of light in glass (n=1.5) is 2×10⁸ m/s. The refractive index of liquid is
📅IOM 2014
Q8.
Which correctly shows regions of the electromagnetic spectrum in order of increasing wavelength?
📅KU 2014
Q9.
Which part of the EM spectrum has frequency > infra-red and wavelength < X-ray?
📅KU 2014
Q10.
A light wave has a frequency of 100 Hz. The wavelength of the wave is:
📅IE 2011
Q11.
Which has lower energy than infrared waves?
📅IE 2013
Q12.
The velocity of light in vacuum depends upon
📅IE 2012
Q13.
In Fizeau's experiment (720 teeth, d=9.633 km, 750 rpm), speed of light is
Q14.
In Foucault's experiment (r=20m, 20 rps), angle of rotation is
Q15.
In Michelson's experiment, if distance between mirrors is doubled, speed of octagonal mirror should be