Is Snell's Law valid even when incident ray is Normal to the surface?

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Discussion Overview

The discussion revolves around the validity of Snell's Law when the incident ray is normal to the surface of a lens or any refracting surface. Participants explore the implications of this scenario on the mathematical formulation of Snell's Law, particularly focusing on the conditions under which it can be applied.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant notes that applying Snell's Law as n21 = sin i / sin r leads to an indeterminate form (0/0) when the incident light is normal to the surface.
  • Another participant presents the equation n1 sin θ1 = n2 sin θ2 as the correct formulation of Snell's Law, implying that the sine terms should not be zero.
  • A subsequent post reiterates the same equation and questions which formulation is the "actual" Snell's Law, highlighting the confusion over the two expressions.
  • One participant emphasizes that the formulation n1 sin(i) = n2 sin(r) is not valid when sin(r) equals zero, suggesting a limitation in the application of Snell's Law in this context.

Areas of Agreement / Disagreement

Participants express disagreement regarding the correct formulation of Snell's Law and its applicability when the incident ray is normal to the surface. No consensus is reached on how to handle the situation mathematically.

Contextual Notes

The discussion highlights the potential for confusion arising from the mathematical treatment of Snell's Law in edge cases, particularly regarding the assumptions made about the sine functions involved.

aleemudasir
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According to the Snell's Law refractive index n21= sin i/sin r, but when we use this equation while having a incident light normal to the surface of lens or any other refracting surface it becomes 0/0. So how can we define Snell's law in this situation?
 
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n_1sin\theta_1 = n_2sin\theta_2

This is the actual Snell's law. When you shift the sin over to the other side, you assume it's not 0.
 
Infinitum said:
n_1sin\theta_1 = n_2sin\theta_2

This is the actual Snell's law. When you shift the sin over to the other side, you assume it's not 0.

Which one is the actual n21=sin i /sin r or n1 sin i= n2 sin r?
 
As I said above...

n_1sin(i) = n_2sin(r)

The other one is not valid when sin(r) is equal to zero.
 

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