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A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water (Fig. P33.55). The refractive index of the plastic wall is 1.61. If the light that has been reflected from the wall into the water is observed to be completely polarized, what angle does this beam make with the normal inside the water?

Short Answer

Expert verified

The angle this beam makes with the normal inside the water is23.3 .

Step by step solution

01

About Brewster’s Law.

The light could be polarized by total reflection. This is Brewster鈥檚 law which states that if the incident angle equals the polarized angle, the light will be polarized. The polarization occurs due to reflection. Brewster鈥檚 law is given by

tanp=nbna

Where nbis the refractive index of the plastic wall whilena is the refractive index of air and it equals 1 Now, substitute the values forna andnb into equation to getp

b=tan-1nbna=tan-11.611=58.15

As we mentioned above, the incident angle at the wall equals the polarized angle.

So, we can consider this angle to be the angle of the incident at the wall. Hence the incident angle on the watera will be

a=90-58.15=31.85

When the light is reflected and travels to the water, the refraction occurs where the refractive index of water is nW. The refractive index of an optical material is expressed by n and the speed of light in the vacuum divided by the speed of light in the material. Snell鈥檚 law is given in the form

nasina=nwsinw

Now substitute the valuesnw,na anda .

b=sin-1nasinanw=sin-11sin31.851.333=23.3

02

Conclusion.

Hence, the angle this beam makes with the normal inside the water is23.3 .

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