Time lost by light in any medium w.r.t vacuum

TIME LOST BY LIGHT IN ANY MEDIUM WITH RESPECT TO VACUUM

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.

CALCULATION

Consider a light beam of any frequency traveling in vacuum. Let ‘x’ be the distance traveled by light, the time taken by light to travel this distance is,

t = x/c (Eq. 1)

t – Time taken by light (s)

x – Distance traveled by light (m)

c – Speed of light (m/s)

In any medium X, the speed of light will be,

c’ = c/m (Eq. 2)

c’ – Speed of light in medium (m/s)

m - Refractive index of medium

Time taken by light to travel the same distance x in medium X is,

t’ = mx/c (Eq. 3)

t’ – Time taken by light in medium (s)

If μ ˃ 1, then t’ ˃ t, thus time is always lost.

DT₁ = t’ – t

       = (mx)/c – x/c

       = (x/c)*[m - 1] (Eq. 4)

CONCLUSION

The above expression gives idea about time lost by light with respect to vacuum. The time loss is independent of frequency but depends on the speed of light. We can observe that time is always lost in all mediums of refractive index greater than 1.