Ray optics made refraction rustic enough, as path of the light is represented by a straight line. This paves in surplus excitement to the human mind in search of rationale for every thing that it can conceive.
1) The speed of light in rarer(1) and denser(2) medium be v and c respectively.
2) For the sake of brevity light ray travel for same time in both the medium.
Logical offsets :
i > r
i,r <= 90 deg
Therefore,
Sin(i) > Sin(r)
The introduction of sine function as the consequence of Snell's law, where
Sin(i)/Sin(r) = n
n = (x1/x2)*(d2/d1)
= (x1/x2)*((d2/t)*(t/d1))
= (x1/x2)*(v/c)
"Light ray travelling for same time in both the medium" was very much essential for the mathematical frame work for the three equations above. Lets analyse what happens if times were not equal.
Now I will change adjustment 2) -> 2') (I will put it as adjustment rather than assumption).
2') Light travels for time t1 in medium (1) and time t2 in medium (2).
Rationale A :
Even if t1 not equalling t2 the ratio v/c do not get altered.
This is 'physical' argument which steers the mathematical frame work.
Therefore,
n = (x1/x2)*((d2/t2)*(t1/d1))
= (x1/x2)*(d2/d1)*(t1/t2)
Rationale B :
From 2') Light travels for time t1 in medium (1) and time t2 in medium (2).
n = (x1/x2)*((d2/t2)*(t1/d1))
= (x1/x2)*(d2/d1)*(t1/t2)
The above steps are mathematically inconsistent, because I am introducing a new ratio (t1/t2), where t1 not equalling t2, yet I am claiming it to equal 'n'.
Perspective :
Can rationality of human thought conceive every thing the nature provides ?
This makes me wonder, even if the laws of nature may be written in the language of mathematics but the limitations of the language nests the loss of many things which go untold.
1) The speed of light in rarer(1) and denser(2) medium be v and c respectively.
2) For the sake of brevity light ray travel for same time in both the medium.
Logical offsets :
i > r
i,r <= 90 deg
Therefore,
Sin(i) > Sin(r)
The introduction of sine function as the consequence of Snell's law, where
Sin(i)/Sin(r) = n
n = (x1/x2)*(d2/d1)
= (x1/x2)*((d2/t)*(t/d1))
= (x1/x2)*(v/c)
"Light ray travelling for same time in both the medium" was very much essential for the mathematical frame work for the three equations above. Lets analyse what happens if times were not equal.
Now I will change adjustment 2) -> 2') (I will put it as adjustment rather than assumption).
2') Light travels for time t1 in medium (1) and time t2 in medium (2).
Rationale A :
Even if t1 not equalling t2 the ratio v/c do not get altered.
This is 'physical' argument which steers the mathematical frame work.
Therefore,
n = (x1/x2)*((d2/t2)*(t1/d1))
= (x1/x2)*(d2/d1)*(t1/t2)
Rationale B :
From 2') Light travels for time t1 in medium (1) and time t2 in medium (2).
n = (x1/x2)*((d2/t2)*(t1/d1))
= (x1/x2)*(d2/d1)*(t1/t2)
The above steps are mathematically inconsistent, because I am introducing a new ratio (t1/t2), where t1 not equalling t2, yet I am claiming it to equal 'n'.
Perspective :
Can rationality of human thought conceive every thing the nature provides ?
This makes me wonder, even if the laws of nature may be written in the language of mathematics but the limitations of the language nests the loss of many things which go untold.
