Question

Light is incident normally on the short face of a 30∘−60∘−90∘ prism (Figure 1). A drop of liquid is placed on the hypotenuse of the prism.
a) If the index of the prism is 1.50, find the maximum index that the liquid may have for the light to be totally reflected.
Express your answer using three significant figures.

Answer 1

1.06 is the maximum refractive index that the liquid may have for the light to be totally reflected.

Only when a light source passes from a denser to a rarer medium can it completely reflect.

When the angle of incidence surpasses a specific critical value, specular reflection occurs in the more highly refractive of the two mediums at their interface, and this reflection is known as total reflection.

sin $i_{c}$ = μ$_{r}$ / μ$_{d$

From the diagram

Angle of incidence = 60°

sin60°  ≥ sin$i_{c}$ = μ$_{r}$/μ$_{d}$

μ$_{r}$ ≤ μ$_{d}$ sin60°

μ$_{r}$ ≤ √1.5 × √3/2

   = 1.06

Hence, the maximum index that the liquid may have for the light to be totally reflected is 1.06

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