For the same value of angle of incidence the angle of refraction in three media A,Band C are 15 degree,25 degree and 35 degree respectively.in which medium the velocity of light be minimum?
We know that velocity of light in amedium is inversely proportional to the refractive index of the medium from the equation
n = c / v .............(1)
Moreover the refractive index of the medium is inversely proportional to the angle of refraction for the same angle of incidence from the equation
n = sin i / sin r ..............(2)
From (1) and (2) ,it is clear that velociy of light in a medium is directly proportional to the angle of refraction in that medium at a particular angle of incidence.
Thus the velocity of light is minimum in medium A where the angle of refraction is minimum.
also n=sin i/sin r
which implies, sin i/sin r = c/v
since both c and sin i are constant (c is the speed of light in air, and according to the question, it says, its the same angle of incidence)
therefore, v = sin r
Since, sin 15 < sin 25 < sin 35
Hence, the velocity of the light will be minimum in medium A.
refractive index is given by
for a given angle of incidence, angle of refraction is less in a medium compare to other medium means refractive indexof that medium is more.
hence in the given problem medium A is giving minum angle of refraction 15°. Hence refractive index of medium A is highest.
if refractive index is maximum in medium A means, speed of light is minimum in medium A
When refractive index is high then angle of refraction will be less as ray bends towards normal.
Therefore refractive index of medium A will be more since the angle of refraction in it us the least.
And since refractive index of medium A is highest then velocity will be lowest or minimum in it.
Therefore the answer: medium A