Air wedge interference pattern after being filled with water

[Andrew Tom]

Homework Statement

Air wedge interference pattern after being filled with water

Relevant Equations

$x=\frac{\lambda}{2\tan \theta}$

An air wedge is illuminated with light and an interference pattern is produced. What will happen to the interference pattern when the air wedge is filled with water?

The answer given at the back of the book is that the fringe spacing of the interference pattern will increase, however my reasoning is leading me to the conclusion that it will decrease.

The derivation for fringe spacing given in the book for an air wedge shows that it is $\frac{\lambda}{2\tan \theta}$ where $\theta$ is the wedge angle. When I re-derived the formula using the same reasoning but for water with refractive index n I got the fringe spacing $\frac{\lambda}{2n\tan\theta}$. So the fringe spacing will decrease because n>1 for water.

 

[haruspex]

the interference pattern will increase

Are those the exact words? I don't know what that means.

 

[Andrew Tom]

Are those the exact words? I don't know what that means.

Sorry it says the fringe spacing will increase.

 

[haruspex]

Sorry it says the fringe spacing will increase.

I agree with you. A higher refractive index would mean you don't need to go so far along the wedge for the optical path length to increase by a wavelength.

 

[Andrew Tom]

I agree with you. A higher refractive index would mean you don't need to go so far along the wedge for the optical path length to increase by a wavelength.

So is the book wrong?

 

[haruspex]

So is the book wrong?

I would say so. Others may chip in.