# Refraction at normal incidence

• Gobil
In summary, a beam of light passing through a material with a variable index of refraction will experience a phase shift, but the direction of the wave will not change.

#### Gobil

high All,

Just got to thinking, if we have a beam of light normal to a flat surface, and the surface is that of an object which has a variable refractive index across the transverse beam direction, will some of the light be bent away from the normal on the other side of the object?

i.e. if we have a ´flat´lens, with a distribution (lets say Gaussian) of refractive indices in the material transverse to the beam direction, will it act as a normal lens and focus or defocus the beam?

I understand the refractive index causes a phase-shift in the EM waves, but does this also change direction as in the example I describe above?

Many Thanks!

Andy Resnick said:

Counterintuitive for me

ok, thanks.

But when we talk about the real part of the refractive index changing the phase of the EM wave, do we mean the phase is just changed in the plane of (original) propagation? i.e. it doesn´t really change the phase, but just the propagation direction, and hence if you observe all the phases relative to the plane of incidence they have changed?

..but wait, if the light propagates through a uniform block of glass at normal incidence, there will be a phase change.. confused.

I'm not sure what you are asking- taking the initial phase of the wavefront as 'zero', making a uniform change to the phase does nothing, but making a spatially-dependent phase change does do a lot- you can convert a plane wave to a converging wave, for example.

Or am I not understanding you?

well, what I mean is if you propagate 2 beams parallel to each other, one through vacuum, and the other through some uniform medium with a finite refractive index and finite length, will there be a difference in phase between the two waves when they are measured after the block?

yes- that's the principle of a Mach-Zender interferometer.

ok, so when we have a uniform block of material and a beam passing through it at normal incidence we have refraction in the form of a phase change of that EM wave. when this medium has a gradient of refractive index transverse to the beam we get a change in wave vector, i.e. the direction of the beam, and also a change in phase, is this correct?

Yes, but they are equivalent- a spatially varying change of phase is equivalent to a change in propagation direction; consider the form exp (ikz), and now let k = k + d(x,y), where d is the amount of phase change. If d(x,y) = d_0, you get an overall constant phase shift (interferometer). If d(x,y) = (x/r)^2 + (y/r)^2, you get a converging spherical wave (if I wrote d correctly...). Thus, a uniform block of glass of varying thickness (say, a lens) is equivalent to a flat slab of glass with a gradient refractive index.

great thanks,

so this is the key point, a uniform change in phase (in a uniform medium) will cause phase shifts in the wave, but no directional change. But if the RI varies across the transverse of the beam, the change in phase is different for the different parts of the beam. I have an image in my head of an EM wave having different phase shifts at one 'side' of the amplitude wave the the other, and when this happens, it is essentially bent to the 'faster' area of the medium.

does this sounds right?

Gobil said:
I have an image in my head of an EM wave having different phase shifts at one 'side' of the amplitude wave the the other, and when this happens, it is essentially bent to the 'faster' area of the medium.

does this sounds right?
Except that the beam is bent toward the slower (higher refractive index) area of the medium.

## 1. What is refraction at normal incidence?

Refraction at normal incidence is the phenomenon of light traveling through a transparent medium and changing direction when it passes from one medium to another at a 90 degree angle (normal incidence).

## 2. What causes refraction at normal incidence?

Refraction at normal incidence is caused by the change in speed of light as it travels from one medium to another. The change in speed is due to the difference in the optical density of the two mediums.

## 3. How does the angle of incidence affect refraction at normal incidence?

The angle of incidence does not affect refraction at normal incidence, as the light is passing through the mediums at a 90 degree angle. This means that the angle of refraction will be equal to the angle of incidence.

## 4. What is the law of refraction at normal incidence?

The law of refraction at normal incidence, also known as Snell's law, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the first medium to the speed of light in the second medium.

## 5. How is refraction at normal incidence used in everyday life?

Refraction at normal incidence is used in various everyday applications, such as in the lenses of glasses and cameras, which use refraction to focus light. It is also used in prisms to split white light into its component colors and in fiber optics for telecommunication.