Download Chapter 32 Problem 51 † Given d = 0.065 mm λ = 550 nm Solution

Chapter 32
Problem 51
†
Given
d = 0.065 mm
λ = 550 nm
Solution
Find the number of bright bands formed on the plate.
The thin film in this problem is the air between the two glass plates. The index of refraction is 1.000.
The light reflecting off the top of the air wedge will undergo a 0◦ phase change since the light is entering
a less optically dense material. The light reflecting off the bottom of the air wedge will undergo a 180◦
phase change since the glass is more optically dense than the air. Therefore, for a bright spot the light
must travel a half integer wavelength in the air wedge in order to constructively interfere. This leads to
the formula
2n · d = (m + 12 )λ
Solving for the value of m gives
m=
2n · d 1
−
λ
2
When the slides are touching, the distance is zero and we have a minimum value of m = −1/2. At the
other end where the paper is holding the glass slides apart the value of m is
m=
2(1.000)(65000 nm) 1
− = 235.9
550 nm
2
Since there is only bright bands at the integer values of m, m can have the values of 0 through 235. This
gives a total of 236 bright bands.
†
Problem from Essential University Physics, Wolfson