# How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to...

## Question:

How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 540 mm light is incident normally?

{eq}T_{min} {/eq} = _____ m

What if the glass is to appear dark?

{eq}T_{min-} {/eq} = _____ m

## Interference:

Interference is a phenomenon in which two waves interact and superimpose each other. If the waves that superimpose are in-phase, then this form a resultant wave of higher amplitude, this is called constructive interference. Destructive interference is when two waves that superimpose are out-of-phase and forming a resultant wave of lower amplitude.

Given:

{eq}\lambda = 540 \ mm = 540 \times 10^{-3} \ m {/eq}

Part A) For the glass to appear bright, then a constructive interference must have taken place. The formula for the minimum thickness for constructive interference is given by,

{eq}2 t = (m + \frac {1}{2}) \lambda {/eq} where m = 0

Solving for t,

{eq}t = \frac {(m + \frac {1}{2})\lambda}{2} = \frac {(0 + \frac {1}{2})(540 \times 10^{-3} \ m)}{2} = \boxed {0.135 \ m} {/eq}

Part B) For the glass to appear dark this time, then it is destructive interference that took place. The formula for the minimum thickness for destructive interference is given by,

{eq}2 t = m \lambda {/eq} where m = 1

Solving for the thickness t,

{eq}t = \frac {m \lambda}{2} = \frac {1 (540 \times 10^{-3} \ m)}{2} = \boxed {0.27 \ m} {/eq}