Question

8. A light ray enters a rectangular block of a newly created plastic material and travels along the path shown below. By considering the behavior of the ray at point P, determine the speed of light in the plastic. What is the critical angle for this new plastic? Determine what will happen to the light ray when it reaches point Q. Does it refract or reflect and at what angle? a. b. c. P37 Air Plastic 53°

Answer 1

The angle between the Normal and the Incident Ray is called the Angle of Incidence = ( 90 - 37) = 53 degree

The angle between the Normal and the Refracted Ray is called the Angle of Refraction = ( 90 - 53) = 37 degree

(a) According to Snell's Law,

n₁ sin i = n₂ sin r , n₁ = 1 , index of refraction of air as the incident ray is in air

On substituting the values,

1 sin (53) = n₂ sin (37)

n₂ = sin (53) / sin (37)

c/v = sin (53) / sin (37) , v is the speed of light in plastic

v = c [sin (37) / sin (53)]

v = c ( 0.75)

v = 75% the speed of light

(b) Critical angle - The angle at which the incident ray after refraction makes 90 degree with the normal.

Implies, sin r = sin 90 = 1

Hence, Snells law reduces to--

n₁ sin x = n₂ sin 90

1 sin x = n₂ , x is the critical angle

n₂ = c/v = c/ 0.75c = 1/0.75 = 1.33 = sin x

x = sin inverse ( 1.33) , Contradiction

Hence , total internal reflection doesn't occur when light travels from a low refractive index to a high index medium .

(c) When a ray of light passes from a less dense material (air) into a more dense material ( plastic) it is bent away from the surface between the two materials, Angle of Refraction ( 37 degree) is less than the Angle of Incidence ( 53 degree)

And,

When a ray of light passes from a more dense material ( plastic) into a less dense material (air) it is bent towards the surface between the two materials, Angle of Refraction is more than the Angle of Incidence.

Again , Using Snell's Law,

n₁ sin i = n₂ sin r , n₁  (Refractive Index for Plastic) = 1.33 n₂  (Refractive Index for Air ) = 1

1.33 sin (53) = 1 sin r , Angle of incidence is 53, Considering PQ be the transversal for the two parallel lines

we apply alternate interior angles,(Angle pair on the opposite side of the transversal and the interior of the parallel lines are equal.)

1.33 * 0.7986 = sin r

sin r = 0.94

r = sin inverse (0.94) = 70 degree

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