Lecture 28, Wednesday April 15

Diffraction GratingThin Film InterferenceSingle Slit Diffraction

Problems due Today

• 17: 13, 17, 19, WB 25: 1-18• 13: diffraction grating• 17: ditto• 19: skip b• WB 17: 1-9 pictures of interference• 25: 19, 22, 28, 29, 31

Two slit interference

• Young demonstrated light behaved as a wave.• Bright fringes occurred at angles

• For small angles

sin mm d

0,1,2,3,...

m

m

mdm Ly md

QUIZ # 9

Two narrow slits 0.04 mm apart are illuminated by light from a HeNe laser (λ = 633 nm). A. What is the angle of the first (m = 1) bright fringe?B. What is the angle of the thirtieth bright fringe?

Slide 17-11

Index of Refraction—cf. Lab last week

• Index of refractionspeed of light in vacuumspeed of light in material

mat vac

vacmat

cnv

v f c fv cf nf n

The Diffraction Grating

Slide 17-12

The Intensity Pattern Due to a Diffraction Grating

Slide 17-14

The Fringes Become Very Narrow as the Number of Slits is Increased

Slide 17-15

A Diffraction Grating Splits Light into the Wavelengths That Make It Up

Slide 17-16

All waves spread out after passing through a small enough gap in a barrier. This phenomenon is

known as

Anti

reflec

tion

double-

slit in

...

Refr

actio

n

diffra

ction

25% 25%25%25%1. Antireflection2. double-slit

interference3. Refraction4. diffraction

Problems due Friday

• 17: 1, 2, 4, 7, 9, 10, 12• 2: speed in glass• 4: wavelength in glass• 7: two slit interference• 9: ditto, given d and y5 – y1, find λ• 10: two slits given fringe spacing, λ• 12: Δr

Problems

• 25: 19 E = 10 V/m in an electromagnetic wave. What is B?

• 22:

– What is λ, f, and electric field amplitude?• 28: I = 10 W/m2 for a linearly polarized wave.

Intensity through polarizer with b) θ = 300 ?

8( , ) (20 / )sin((6.28 10 ) 2 )yE x t V m x x ft

More Problems

• 29: 25% passes polarizer. Angle of polarizer with respect to electric field?

• 31: Unpolarized light with I = 350 W/m2 – What is I after two polarizers with second axis 350

to axis of first?

Problems 17

• CQ1: frequency in water, glass• CQ3: change in λn , does it change apparent

color?• MC17: what changes when light enters glass?• 1: travel time through piece of glass

Thin-Film Interference

Slide 17-17

Phase Changes Due to Reflection

Slide 17-18

Analyzing Thin-Film Interference

Slide 17-19

Single-Slit Diffraction

Light passing through a narrow slit spreads out beyond the slit.

Slide 17-23

Analyzing Single-Slit Diffraction

Slide 17-24

Single-Slit Diffraction: Positions and Intensities

Slide 17-25