37.5 Change of Phase Due to Reflection n1 n2 0 n 0 nhuang24/Teaching/Phys2401/LectureNotes/CH37B.pdfDetermine the minimum film thickness that produces the least reflection at a wavelength

37.5 Change of Phase Due to Reflection A wave traveling from a medium of index of refraction n1

toward a medium of index of refraction n2 undergoes a 180° phase change upon reflection when n2 > n1. There is no phase change in the reflected wave if n2 < n1.

37.6 Interference in Thin Films

Why thin films of oil on water and soap bubbles displays color patterns?

Review: The wavelength of light !n in a medium whose

refraction index is n is

!

"n ="0n

, where !0 is the wavelength of

light in free space. • The condition for constructive interference in soap bubble films

is 2t = (m + 12)!n

!

2nt = (m+ 12)"0 (m = 0, 1, 2, )

This takes into account (1) differences in the distances traveled by two rays and (2) phase changes that occur upon reflection.

• The condition for destructive interference in soap bubble films is

2nt = m! (m = 0, 1, 2, )

• The color pattern is due to variation of thickness of films. Newton's Rings

Example: Calculate the thickness of a soap bubble film (n = 1.33) that results in constructive interference with 600 nm light. Solution: For constructive interference:

2nt = (m + 12)! (m = 0, 1, 2, )

Thus, t =(m + 1

2)!2n

=(m + 1

2)600nm2(1.33)

= (m + 12)225.6nm

t = 113 nm, 338 nm, 789 nm, and so on. Example: Non-reflective coating for solar cells.

A transparent thin film of silicon monoxide (SiO, n = 1.45) is coated on the surface of a solar cell (n = 3.5) to minimize reflective losses. Determine the minimum film thickness that produces the least reflection at a wavelength of 550 nm, near the center of the visible spectrum. Solution: Reflected bean #1 and #2 must have destructive interference. Since both beams have 180° phase change, the condition for the destructive interference is

!

2t = (m+ 12)"SiO = (m+ 1

2)" /nSiO For the minimum thickness, m = 0

!

t = " / 4nSiO = 550nm /(4 #1.45) = 94.8 nm

Michelson Interferometer • A ray of light is split into two rays by the mirror Mo. • The mirror Mo is at 45o to the incident beam. The mirror is called

a beam splitter. It transmits half the light and reflects the rest. • The reflected ray goes toward mirror M1. • The transmitted ray goes toward mirror M2. • The two rays travel separate paths L1 and L2. • After reflecting from M1 and M2, the rays eventually recombine

at Mo and form an interference pattern. The interference condition for the two rays is determined by their path length difference.

• As M1 moves, the fringe pattern collapses or expands, depending on the direction M1 is moved.

• The fringe pattern shifts by one-half fringe each time M1 is moved a distance !/4.

• The wavelength of the light is then measured by counting the number of fringe shifts for a given displacement of M1.

Applications:

The Michelson interferometer was used to disprove the idea that the Earth moves through an ether.

Modern applications include: * Fourier Transform Infrared Spectroscopy (FTIR) * Laser Interferometer Gravitational-Wave Observatory (LIGO)

• Einstein predicted the existence of gravitational waves. In his theory, gravity is equivalent to a distortion of space.These distortions can then propagate through space.

• The LIGO apparatus is designed to detect the distortion produced by a disturbance that passes near the Earth.

• The interferometer uses laser beams with an effective path length of several kilometers.

• At the end of an arm of the interferometer, a mirror is mounted on a massive pendulum.

• When a gravitational wave passes, the pendulum moves, and the interference pattern due to the laser beams from the two arms changes.