Diffraction, Grating, Resolving Power - Lecture Slides | PH 113, Study notes of Advanced Physics

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Chapter 36:

Diffraction, Gratings,

Resolving Power

Physics 113 Dr. Renat Letfullin

Today:

• Diffraction of the light

• Single Slit Diffraction

• Diffraction from Circular Aperture

• Diffraction Gratings

• Resolving Power

• Help Session for the Test #3.

Wall Screen with opening (or obstacle without screen) shadow bright

This is not what is

actually seen!

Diffraction Rays

Physics 102: Lecture 20, Slide 5

Diffraction/ Huygens

Every point on a wave front acts as a source of tiny wavelets that move forward. We will see maxima and minima on the wall. Light waves originating at different points within opening travel different distances to wall, and can interfere!

W

w 2 sin

W 2

Rays 2 and 2  also start W/2 apart and have the same path length difference.

st minimum at sin  = /w When rays 1 and 1  interfere destructively. w 2 sin   2 Under this condition, every ray originating in top half of slit interferes destructively with the corresponding ray originating in bottom half.

Single Slit Diffraction

w Rays 2 and 2  also start w/4 apart and have the same path length difference. 2 nd minimum at sin  = 2/w Under this condition, every ray originating in top quarter of slit interferes destructively with the corresponding ray originating in second quarter.

Single Slit Diffraction

4 w

sin( ) 4 w 

When rays 1 and 1  will interfere destructively. 2 sin( ) 4 w   

Light from a He-Ne laser ( = 633 nm) passes through a narrow slit and is seen on a screen 2.0 m behind the slit. The first minimum in the diffraction pattern is 1.2 cm from the central maximum. How wide is the slit?

Light passes through a 0.12-mm- wide slit and forms a diffraction pattern on a screen 1.0 m behind the slit. The width of the central maximum is 0.85 cm. What is the wavelength of the light?

Maxima and minima will be a series of bright and dark rings on screen Central maximum

sin  1. 22

D

First diffraction minimum is at  Diameter D light

Diffraction from Circular Aperture

1 st diffraction minimum Physics 113 Dr. Renat Letfullin

sin   

D

L

Y

1

I

Intensity from Circular Aperture

First diffraction minima

Conceptual question

A laser is shone at a screen through a very small hole. If you make the hole even smaller, the spot on the screen will get: (1) Larger (2) Smaller Which drawing correctly depicts the pattern of light on the screen? (1) (2) (3) (4) Physics 113 Dr. Renat Letfullin

Light from a He-Ne laser ( = 633 nm) passes through a 0.5-mm- diameter hole. How far away should a viewing screen be placed to observe a diffraction pattern whose central maximum is 3.0 mm in diameter? Physics 113 Dr. Renat Letfullin

N slits with spacing d Constructive Interference Maxima are at:

sin m

d

• screen VERY far away 

Diffraction Grating

Same as for Young’s Double Slit! Physics 113 Dr. Renat Letfullin

Light from a sodium light passes through a

diffraction grating having 1000 slits per

millimeter. The interference pattern is

viewed on a screen 1.0 m behind the grating.

Two bright yellow fringes are visible 72.

cm and 73.0 cm from the central maximum.

What are the wavelength of these two

fringes?

Physics 113 Dr. Renat Letfullin