Answer:
Critical angle , c =sin^-1(1/n) and refractive index (n) = 1.5 proved.
Explanation:
We have to explain critical angle and refractive index.
(a).
(i).
Critical angle (c) :
An angle of incidence,whenever a light ray passes through denser medium to rarer at which the angle of refraction to the rarer side is 90 degrees.
Rarer medium:
Where the speed of light is more comparatively.
Formula:
In terms of refractive index (n).
⇒ [tex]c=sin^-^1(\frac{1}{n} )[/tex]
Here the shoe lace is the denser medium and light going out of this plastic shoe laces to air will have a critical angle at the boundary of the two media (plastic-air) if and only if the angle if refraction is 90 degree.
(ii).
Refractive index (n) :
Is the ratio of speed of light in vacuum (c) to tat of speed of the light in medium (v).
⇒ And [tex]c = 3\times 10^8[/tex] m/s
⇒ [tex]n=\frac{c}{v}[/tex]
⇒ [tex]n=\frac{3\times 10^8}{v}[/tex]
⇒ [tex]n=\frac{3\times 10^8}{1.97\times 10^8}[/tex] ...speed of light in plastic,v = [tex]1.97\times 10^8\ ms^-^1[/tex]
⇒ [tex]n=1.5[/tex]
As mentioned the refractive index = 1.5
Refractive index is dimensionless quantity.
