Question

The critical angle for a substance is measured at 53.7°. Light enters from air at 45° . What is the refractive angle?

Answer 1

The hypothetical answer is 61,32 degrees, found from application of Snell's Law in optics, but the figures in the question make the final answer unrealistic due to implication that light travels faster in the medium than in air. Details in sketch below.

Explanation:

Answer 2

I have added as a new answer since not enough characters given in edit to allow my full explanation.

Explanation:

Yes unfortunately it does. You see, by definition, the index of refraction n of a medium is a ratio of the speed of light in air r vacuum to the speed of light in the medium. (n=c/v). So basically the value of n tells you how may times faster light travels in air as compared to the medium. Example, n for most glass is about 1,5. This means that light travels 1,5 times aster in air than in glass. So if n is less than 1, like 0,8 in his question, it means light travels faster in the medium than in air. But by Einstein's theory this is impossible since light always travels fastest in air or vacuum, 3x10^8 m/s, and nothing can travel faster than light, else it will become invisible and time will stop for it according to relativity theory. Therefore this question is faulty in everyday domain. (Unless you want o apply it to quantam domain, but that is well beyond the scope of undergraduate level).

Answer 3

`r=34.4^0`

Explanation:

Refractive index is given by:

`mu=sini/sinr`

When `r=c` that is called the critical angle. Thus `i=90^0` and `sini=sin90=1`.

So:

`mu=sin90/sinc=1/sinc`

Where `c` is the critical angle.

`mu=(1)/(sin53.7)=(1)/(0.8)=1.25`

`mu=(sini)/(sinr)`

`sinr=(sini)/(mu)=(sin45)/(1.25)=(0.707)/(1.25)=0.565`

From which:

`r=34.4^0`

Remember light slows down when entering a denser medium and the angle of refraction is always less than the angle of incidence.

The reverse will be true if the light is going the other way.