Porro prism and Refraction of Light

[Nano]

Homework Statement

Ligh is incident normally upon one face of a prism of glass with an index of refraction, n. The light totally reflected as shown in the picture*. What is the minimum value n can have?

*Picture shows a Porro prism (45-45-90 prism)

Homework Equations

n sin(a) = n2 sin (b)
setting b = 90 will solve for the critical angle

The Attempt at a Solution

I guess it has something to do with critical angles. I just don't know how to use the information given. If its incident normally, then does sin(a) = 0? And if the light is not totally internally reflected then, the index of refraction for the prism must be greater than the index of refraction for air (1). so n(prism) > 1.

 

[rl.bhat]

In the porro prism, when the light enters from the smaller side normally, it move without refraction and it incidents on the hypotenuse making an angle of incidence 45 degrees. If this angle happens to the critical angle of the prism glass then the refractive index is given by n = 1/sin(45)

 

[nlightner]

I would like to clarify some points regarding this scenario. Firstly, the phenomenon described is known as total internal reflection, which occurs when light travels from a medium with a higher refractive index to a medium with a lower refractive index at an angle of incidence greater than the critical angle. In this case, the light is traveling from the glass prism (with a refractive index of n) to air (with a refractive index of 1). Therefore, the minimum value of n would be 1, as any value lower than 1 would result in the light not being totally internally reflected.

Furthermore, the equation n sin(a) = n2 sin(b) is known as Snell's law, which describes the relationship between the angle of incidence (a), the refractive index of the first medium (n), the angle of refraction (b), and the refractive index of the second medium (n2). However, in this scenario, we are not concerned with the angle of refraction as the light is being totally internally reflected. The critical angle, as you correctly mentioned, can be found by setting b = 90 degrees in Snell's law.

To summarize, the minimum value of n in this scenario would be 1, and the critical angle can be found by setting b = 90 degrees in Snell's law. I hope this helps in understanding the concept of total internal reflection and its application in this scenario.