How does LLoyd's mirror works?

[KFC]

I wonder how does Lloyd's mirror works, how does it produce the interference pattern? I look for many textbook, but all of them only tells the result and the setup without telling how to get the fringe and how to get the fringe separation. Anyone show me some hint or recommend me a book about this?

Thanks.

 

[Andy Resnick]

From what I saw online, it looks like a shear plate interferometer- I make them with optical flats in the lab to observe the wavefront.

Basically, it's just like a michaelson interferometer- on my setup, one arm is formed by the reflection off the first surface, and the second arm is formed by the reflection off the back surface of the flat (or glass slide, which is fairly flat).

 

[Dadface]

I wonder how does Lloyd's mirror works, how does it produce the interference pattern? I look for many textbook, but all of them only tells the result and the setup without telling how to get the fringe and how to get the fringe separation. Anyone show me some hint or recommend me a book about this?

Thanks.

It's a plane mirror illuminated, usually, by a slit source.The direct waves and the reflected waves overlap to produce a Youngs type interference pattern.The reflected waves undergo a phase change of Pi.It's like having two sources the slit itself and the virtual image
formed by reflection and to get observeable fringes the sources have to be close enough,this will require near grazing incidence and a mirror silvered on its front surface or something equivalent.The slit needs to be parallel to the mirror and the screen at 90 degrees to the mirror and placed at a suitable distance.

 

[KFC]

It's a plane mirror illuminated, usually, by a slit source.The direct waves and the reflected waves overlap to produce a Youngs type interference pattern.The reflected waves undergo a phase change of Pi.It's like having two sources the slit itself and the virtual image
formed by reflection and to get observeable fringes the sources have to be close enough,this will require near grazing incidence and a mirror silvered on its front surface or something equivalent.The slit needs to be parallel to the mirror and the screen at 90 degrees to the mirror and placed at a suitable distance.

Yeah, I feel a bit clear now. But I have two question in your reply. Why we need near grazing incidence? And if this is true, does it mean we can only produce a fringes close to the center of the screen? and why we need the front surface of the mirror be silvered, for providing a pi phase shift? And I wonder if the mirror will always produce a pi phase shift no matter what's the incidence angle is?

I am quite confusing the last statement, what does it mean by "the slit needs to be parallel to the mirror and the screen at 90 degrees to the mirror" ?

 

[Dadface]

Hello KFC,think of this in terms of an ordinary Youngs double slit experiment with visible light and think of the dimensions needed to get observeable fringes.As a rough example the slit separation could be of the order of say one millimetre and the distance to the screen of the order of say one metre In the Lloyds mirror set up the two sources are the single slit and its reflection in the mirror.To get a separation of about one millimetre the single slit has to be extremely close to the mirror with an angle of incidence(measured to the normal)approaching 90 degrees.The problem with an ordinary mirror is that most of the light is reflected from the back silvered surface and because of the thickness of the mirror the distance between the slit and its image will be too large.You may be able to see fringes due to reflection from the front of the glass but the contrast might be too poor(I have never actually done this experiment myself so I am not sure about this).You get a phase change of 180 degrees(0.5 of a wavelength) when light is reflected from a denser medium,in fact I think it was Lloyd who discovered this when he observed that the fringes he expected to be bright were dark and vice versa.