Question

The photograph shows a shoe with novelty shoelaces. light source The laces are long, flexible plastic strands. Light from the light source passes through the tie laces, illuminating the ends. (a) (i) State what is meant by critical angle. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (ii) Show that the refractive index for the plastic used for the laces is about 1.5 speed of light in plastic = 1.97 × 108 m sí

Answer 1

Critical angle , c =sin^-1(1/n) and refractive index (n) = 1.5 proved.

Step-by-step 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).

⇒
`c=sin^-^1((1)/(n) )`

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
`c = 3* 10^8` m/s

⇒
`n=(c)/(v)`

⇒
`n=(3* 10^8)/(v)`

⇒
`n=(3* 10^8)/(1.97* 10^8)` ...speed of light in plastic,v =
`1.97* 10^8\ ms^-^1`

⇒
`n=1.5`

As mentioned the refractive index = 1.5

Refractive index is dimensionless quantity.