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The drawing shows a crystalline slab (refractive index 2.043) with a rectangular cross section. A ray of light strikes the slab at an incident angle of θ1= 37.0°, enters the slab, and travels to point P. This slab is surrounded by a fluid with a refractive index n. What is the maximum value of n such that total internal reflection occurs at point P?

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Okpalawalter8idn

A drawing shows a crystalline slab (refractive index 2.043) with a rectangular cross-section, the maximum value of n   is mathematically given as

nm=1.627

What is the maximum value of n such that total internal reflection occurs at point P?

Generally, the equation for the snells law  is mathematically given as

[tex]n=\frac{sin \theta_1}{sin \theta_2}[/tex]

Therefore

[tex]\theta_2=sin-1(sin35/1.725)\\\\\theta_2=19.42[/tex]

From the image critical angle is

ic=90-19.42

ic=70.58

In conclusion, snells law for total internal reflection

[tex]gn=\frac{sinic}{sin90}[/tex]

sinic=nm/ng

nm=1.725*sin70.58

nm=1.627

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