The drawing shows a crystalline quartz slab with a rectangular cross section. A

Question

The drawing shows a crystalline quartz slab with a rectangular cross section. A ray of light strikes the slab at an incident angle of ?1 = 40, enters the quartz, 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? (nquartz = 1.544)

The drawing shows a crystalline quartz slab with a rectangular cross section. A ray of light strikes the slab at an incident angle of ?1 = 40, enters the quartz, 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? (nquartz = 1.544)

Explanation / Answer

uisng snell's law ,

n * sin@i = nquartz * sin@

n * sin40 = 1.544 * sin@

n = 2.402 *sin@   ........(i)

now for total internal reflection ,

angle of incident will be now = 90 - @

nquartz * sin(90-@) = n * sin90

1.544 * cos@ = n

n = 1.544cos@   ..... (ii)

comparing (i) and (ii) ,

2.402sin@ = 1.544cos@

tan@ = 0.643

@ =32.73 degrees

n = 1.544cos32.73 = 2.402sin32.73 = 1.30

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