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Chapter 36: Q2P (page 1108)

What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at 胃=45掳?

Short Answer

Expert verified

The ratio of the slit width to wavelength is 2.

Step by step solution

01

Write the given data from the question.

For the first diffraction minima, the number of the fringes in the envelope,m=1.

The angle of the diffraction,胃=45掳.

02

Determine the formulas to calculate the ratio of the slit width to the wavelength.

The expression for the minima in the diffraction pattern is given as follows.

asin胃=m位 (1)

Here, ais the slit width, role="math" localid="1663090724172" 位is the wavelength, mis the number of fringes in the envelope, androle="math" localid="1663090789707" 胃 is the angle of diffraction.

03

Calculate the ratio of the slit width to the wavelength.

Derive the expression for the ratio of the slit width to wavelength,

Recall equation (1),

asin胃=m位a位=msin胃

Substitute1 for mand45掳 for 胃into the above equation.

a位=1sin45a位=112a位=2

Hence the ratio of the slit width to wavelength is 2.

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