# Multiple images in a thick mirror

I understand that 4% of the light is reflected back from the glass surface in a thick glass mirror. But why 4%? Why not 5% or 10%? Will this percentage change if the glass has a lower refractive index?

davenn
Gold Member
2021 Award
Where did you read that ? do you have a reference ?

I would expect the percentage to be reflected back from the air/glass boundary surface to be dependant on the quality of the glass and the smoothness of the surface
the rest would be transmitted through the glass and reflected off the rear reflection surface and back out again ( there would be transmission losses in the glass as part of the double traverse the light does as well)

lets see what others have to say :)

Dave

Drakkith
Staff Emeritus
I understand that 4% of the light is reflected back from the glass surface in a thick glass mirror. But why 4%? Why not 5% or 10%? Will this percentage change if the glass has a lower refractive index?

Neglecting surface irregularities and assuming the light strikes at a normal angle (perpendicular to the surface), the amount of light reflected by transparent surface is given by the equation R=(1-n/1+n)2, where R is the amount of light reflected and n is the refractive index. Glass with a refractive index of 1.5 gives us: R=(1-1.5/1+1.5)2, which comes out to be R=0.04, which is 4%.

With a refractive index of 2: R=(1-2/1+2)2, or R=0.111..., which is about 11.1%.

With a refractive index of 1.1: R=1-1.1/1+1.1)2, or R=0.002268, about 0.2%.

Finding the amount of light reflected when the light is striking at an angle other than normal is much more complicated.

• Fiona Rozario and davenn
Neglecting surface irregularities and assuming the light strikes at a normal angle (perpendicular to the surface), the amount of light reflected by transparent surface is given by the equation R=(1-n/1+n)2, where R is the amount of light reflected and n is the refractive index. Glass with a refractive index of 1.5 gives us: R=(1-1.5/1+1.5)2, which comes out to be R=0.04, which is 4%.

With a refractive index of 2: R=(1-2/1+2)2, or R=0.111..., which is about 11.1%.

With a refractive index of 1.1: R=1-1.1/1+1.1)2, or R=0.002268, about 0.2%.

Finding the amount of light reflected when the light is striking at an angle other than normal is much more complicated.

Thank you!

Danger
Gold Member
This is why accurate mirrors as are needed for astronomy and laser work are front-surface reflective.

Drakkith
Staff Emeritus