The speed of light u is equal to c.
Given,
The motion of a transparent medium influences the speed of light.
The water moves with speed v in a horizontal pipe.
Assume the light travels in the same direction as the water moves.
The speed of light with respect to the water is c /n.
The index of refraction of water, n = 1.33
Let us assume u' be the speed of light in water.
u' is related to the refractive index of water,as u' = c/n
where, c is the speed of light.
Let, u be the speed of light in water in the lab frame.
Now, u and u' are related as : u = ( u'+v) /(1+u'v/c^2)
Here, v is the speed of water in the horizontal pipe.
We know the value of u'. so by substituting the value, we will get ,
u = (c/n+v) /(1+cv/nc^2)
u = c/n (1+nv/c) /(1+v/nc)
u in the limit as the speed of the water approaches c.
Thus,
u = lim v-->c [c/n (1+nv/c) /(1+v/nc) ]
u= c/n (1+n) /(1+1/n)
u= c .
Hence, the speed of light u is equal to c.
Learn more about speed here :
brainly.com/question/13943409
#SPJ4
Disclaimer: incomplete question. here is the complete question.
Question:The motion of a transparent medium influences the speed of light. This effect was first observed by Fizeau in1851. Consider a light beam in water. The water moves with speed v in a horizontal pipe. Assume the light travels in the same direction as the water moves. The speed of light with respect to the water is c / n , where n = 1.33 is the index of refraction of water.
(a) Use the velocity transformation equation to show that the speed of the light measured in the laboratory frame isu = c/n (1 + nv/c / 1+ v/nc).
(d) Evaluate u in the limit as the speed of the water approaches c .