PHYS219 Fall semester 2014 Lecture 23: Wave Nature of Light: Thin Film Interference and Diffraction Gratings Dimitrios Giannios Purdue University

PHYS219 through a wormhole

Interference effects in thin films incident light Observations: Ray 2 travels through a longer path than ray 1 If path difference is integer number of wavelengths, then constructive interference results substrate thin film air λ air 2

Reflection off interface with low to high change in index of refraction – 180 o ( π ) phase change Reflection off interface with high to low change in index of refraction –no phase change Must Include Phase Change upon Reflection KEY IDEA Learn to keep track of the phase!! n=1.33 air n=1.00 thin film of water air n= Not to scale Tracking the Phase in Detail

+ + rope Phase change upon reflection? Simple Analogy Take home lesson: phase change upon reflection depends on boundary conditions -

Two ways to produce phase change between two waves: i. One wave travels extra distance ii. A reflection from an optically dense material produces a π phase change upon reflection KEY IDEA

Two contributions to phase difference between Ray 1 and Ray 2: i)Difference in path length between ❶ and ❷ ? (Δx=2t) i)Any phase shifts due to reflection? Assume light is nearly perpendicular to surface of a film which has a thickness t and index of refraction n Analyzing the situation (qualitative) t Not to scale λairλair λ film n

Analyzing constructive interference (quantitative) Condition for complete constructive interference (max. light reflected): KEY IDEA A net 360 o (or 2π) phase difference between two waves produces an in phase condition. Phase difference between ray 2 and ray 1 constructive if here, Δx=2t t λ air λ film because of extra path traveled

Analyzing destructive interference (quantitative) Condition for complete destructive interference (no light reflected): KEY IDEA A net 180 o (or π) phase difference between two waves produces an out of phase condition. Phase difference between ray 2 and ray 1 destructive if here, Δx=2t t λ air λ film

Example I: Thin Film Interference is Everywhere Note: First four illustrations involve thin film of soapy water with air on both sides The color indicates where the wavelength and local film thickness satisfy constructive interference criteria.

Implication: thickness of film must produce constructive interference for red light ( λ ≈650 nm). Physical model: constructive if Calculation: Example I: A region of a soap bubble looks red. What must be its thickness? t λ air λ film Δx=2t

Example II: Antireflective Coatings n glass = 1.52 n air = 1.00 n coating = 1.40 White Light (peak intensity at λ=565 nm) How to minimize reflected light at λ=565 nm?

λ air =565 nm (incident light) In this case, both reflected rays suffer a 180 ◦ (π) phase change upon reflection. Why?? What is implication? these two rays should destructively interfere to reduce reflection t Not to scale Ray 1Ray 1 Ray 2Ray 2 here, Δ x=2t What are possible values for t to minimize reflected light? glass coating air

destructive if Phase difference between ray 2 and ray 1 Destructive Condition Working it out

Reminder: Double slit experiment Not to scale! Side view! Conditions that must be satisfied: Monochromatic: Light with a specific wavelength. Coherent: The phase difference between the light waves arriving at any location remains constant over time. W

More than Two Slits Intensity Pattern Observed on Screen

Incidentλ light Accurately Measuring the Wavelength of Light - Diffraction Gratings - grating to screen distance is W diffraction grating (multiple slits) screen y Not to scale separation between slits = d light fringes (spots) order m = 2 1

The bright spots on a viewing screen are produced by the constructive interference from many, many slits. bright spots or fringes or maxima The underlying physics of the problem is same as before

Where are the bright spots? Bright spots when Spacing between slits is d bright spots or fringes or maxima

Light of unknown wavelength is directed onto a diffraction grating, forming a third order bright fringe which is located on a screen 7.mm from the center bright line. If the distance between the screen and the diffraction grating is 1 m, what is the wavelength of the light? The diffraction grating has 10 slits/mm. Example: a) What is d?

incident light screen diffraction grating m=3 λ Θ b) What is λ ? W=1 m 0 Example: