Evans SPH 4U1

Unit 5: Waves

Note 6: Diffraction of Light through a Single Slit

Reference: Chapter 10.2

Light passing through a single, narrow slit is diffracted.  The narrow the slit, the more diffraction. An interference pattern of bright (maxima) and dark (minima) lines also occurs when a screen is placed on the far side of the slit. The pattern consists of a bright central region (central maxima) with dark regions of destructive interference alternating with progressively less intense bright area (the secondary maxima) on either side.

FOR DIFFRACTION THROUGH A SINGLE SLIT :

Dark fringes appear when:

where W is the width of the slit,  n is the order of the minima, and is the direction of the fringe

Bright fringes appear when:

where W is the width of the slit,  n is the order of the maxima, and is the direction of the fringe

The separation of adjacent maxima or minima is where:

We will prove the three formulas above in class on the overhead (handout of proofs will be distributed)

Important Notes:

~ The width of the central maxima is

~ The smaller the slit width, the larger the distance between maxima and minima.

~ The longer the wavelength, the greater the distance between maxima

~ Also note that diffraction through a single slit is different than interference from 2 point sources.  At first glance their patterns of interference look the same but there are major differences in the formulas.  There are also differences along the centre line....in single slit diffraction the width of the central maxima is (see comparison diagram from class notes  Wed. April 23rd)

Resolution is the ability of an instrument to separate two closely spaced images.  It is limited by the diffraction of light. A small hole (like a lens in a camera/microscope) will have much diffraction and the diffraction from the two images could overlap so much that one cannot resolve the two images.

By  decreasing the wavelength you can increase the resolving power of a microscope since you will get less diffraction (electron microscopes have very small wavelengths).

Example 1:

Green light of wavelength 5.6 x 10-7 m is passed through a single slit of width 0.021 mm. An interference pattern is produced on a screen 75 cm away.

a) What is the distance between the second dark fringe and the sixth dark fringe? (8.0 cm)

b) What is the width of the central bright fringe? (4.0 cm)

Example 2:

Monochromatic light of wavelength 6.8 x 10-7m is passed through a single slit. The third nodal line occurs at an angle of 12 degrees. Find the width of the slit. (9.8 x 10-6m)

Example 3:

Yellow light having a wavelength of 5.8 x 10 -7 m is passed through a single slit which is 0.084 mm wide. An interference pattern is formed on a screen 64 cm away.  How far is the fourth dark band from the central bright band? ( 0.64 m)

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