What is the equation for Snell's Law?

• A. Sin (transmission angle)/Sin (incident angle) = Speed of Medium 2/ Speed of Medium 1
• B. Sin (incident angle)/Sin (transmission angle) = Speed of Medium 1/ Speed of Medium 2
• C. Sin (transmission angle)/Sin (incident angle) = Wavelength of Medium 2/ Wavelength of Medium 1
• D. Tan (transmission angle)/Tan (incident angle) = Speed of Medium 2/ Speed of Medium 1

Answer: (A)

Snell's Law ties how light bends at an interface to how fast light travels in each medium. If we write it in terms of the refractive indices, n1 sin θ1 = n2 sin θ2. Since the refractive index n is c divided by the wave speed v in that medium, we can substitute n = c/v for each medium and cancel the common constant c. This leads to sin θ2 / sin θ1 = v2 / v1. That means the ratio of the sine of the transmission angle to the sine of the incident angle equals the ratio of the speeds of light in the two media. This form is exactly what the option expresses. The relationship also implies sin θ1 / sin θ2 = v1 / v2, and it’s consistent with the usual n1 sin θ1 = n2 sin θ2 form. Physically, if the second medium allows faster light, the transmitted angle increases compared to the incident angle, bending away from the normal.