Time lost by light in different mediums

TIME LOST BY LIGHT IN DIFFERENT MEDIUMS

INTRODUCTION

Light is an electromagnetic wave. It travels with a constant speed of 3 x 10⁸ m/s or 186000 miles/s in vacuum. It is also known as the cosmic constant c. But as the medium changes, the speed of light also changes. When light enters a medium, it undergoes refraction. Refraction is a phenomenon of bending of light. All mediums have a unique value of refractive index μ. Light still continues to move at c but it since it has to move through all the atoms of the corresponding medium, its speed is reduced by a factor of μ of the medium. All of the known mediums like water, glass, oil have μ greater than that of vacuum. For vacuum μ = 1. Thus light travels slowly in all mediums with respect to vacuum. We intend to determine the time lost by light in various mediums with respect to vacuum.

CALCULATION

The general equation for time lost by light is,

DT = (x/c)*[m - 1]

DT - Time lost by light (s)

x – Distance traveled by light (m)

c – Speed of light in vacuum (m/s)

MEDIUM 1: AIR [μ = 1.001]

The time lost in air is,

DT₁ = (x/c)*[1.001 - 1]                                                                  

       = 0.001[x/c] s

MEDIUM 2: WATER [μ = 1.33]

The time lost in water is,

DT₁ = (x/c)*[1.33 - 1]

       = 0.33[x/c] s

MEDIUM 3: GLASS [μ = 1.5]

The time lost in glass is,

DT₁ = (x/c)*[1.5 - 1]

       = 0.5[x/c] s

MEDIUM 4: GLASS, FLINT, 71% LEAD [μ = 1.8]

The time lost in flint glass is,

DT₁ = (x/c)*[1.8 - 1]

       = 0.8[x/c] s

MEDIUM 5: GLASS, ARSENIC TRISULFIDE [μ = 2]

The time lost in arsenic trisulfide glass is,

DT₁ = (x/c)*[2 - 1]

       = [x/c] s

Consider a beam of white light traveling a distance of x = 5 m through all mediums one at a time. We’ll determine the time lost by light in every medium and plot a graph of time lost versus medium to determine the medium where light loses maximum time.

Refractive Index [μ]	Time lost [s]
1.001	1.67E-11
1.33	5.50E-09
1.5	8.33E-09
1.8	1.33E-08
2	1.67E-08

  

GRAPH

EXPLANATION

We can observe that the graph is linear. It means that light will lose more time the as the refractive index increases. In this example light travels for 5 m in different mediums. When light travels through glass it loses around 8.3 nanosecond relative to vacuum and similarly 5.33 nanosecond in water. The loss will increase linearly with the distance traveled by light meaning if light were to travel for 1 year or 1 light year, the light in glass would lose considerable amount of time relative to the light in vacuum.

CONCLUSION

We thus determined the time lost by light in different mediums relative to vacuum.