A fiber-optic rod consists of a central strand of material surrounded by an outer coating. the interior portion of the rod has an index of refraction of 1.55. if all rays striking the interior walls of the rod with incident angles greater than 59.5° are subject to total internal reflection, what is the index of refraction of the coating?

the index of refraction of the coating is 1.33  

Explanation:

Given the data in the question;

refraction index of  interior portion of the rod η = 1.55

angle of incidence θ = 59.5°

From Snell's law, we know that;

η × sinθ  = η × sinθ

where η  is the index of refraction of the rod ( material 1 )

θ  is the angle of incidence

η is the index of refraction in outer coating ( material 2 )

θ is the angle of refraction

so we substitute our values into the equation;

η × sinθ  = η × sinθ

1.55 × sin( 59.5° )  = η × sin( 90° )

1.55 × 0.861629  = η × 1

1.3355 = η × 1

η = 1.33   { 2 decimal places }

Therefore, the index of refraction of the coating is 1.33  

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.