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Chapter 32: Problem 37

A screen \(1.0 \mathrm{m}\) wide is \(2.0 \mathrm{m}\) from a pair of slits illuminated by 633 -nm laser light, with the screen's center on the centerline of the slits. Find the highest-order bright fringe that will appear on the screen if the slit spacing is (a) \(0.10 \mathrm{mm}\) and (b) \(10 \mu \mathrm{m}\)

Short Answer

Expert verified
For the slit spacing (a) \(0.10 \mathrm{mm}\), the highest-order bright fringe is around 3150, and for the slit spacing (b) \(10 \mu \mathrm{m}\), the highest-order bright fringe is around 31500.

Step by step solution

01

Understand the problem and interpret the given data

The pair of slits are exposed to laser light of wavelength 633nm and they are 2.0m away from the screen. Firstly, we need to convert the given measurements into meters.
02

Initialization of variables

Initialize the variables with the given values, like the wavelength \(\lambda = 633 \times 10^{-9} \, m\), the distance from the pair of slits to the screen \(L = 2.0 \, m\), the screen width \(W = 1.0 \, m\), and the slit spacing \(d\) for both (a) and (b) as \(d_a = 0.10 \times 10^{-3} \, m\) and \(d_b = 10 \times 10^{-6} \, m\).
03

Calculate the highest-order bright fringe

The bright fringe order (\(m\)) could be found using the formula \(\frac{m \times \lambda}{d} = \frac{W}{2L}\). Remember, \(m\) must be an integer, so always round down to the nearest integer.
04

Solve for the case (a)

Substitute the values \(\lambda\), \(d_a\), \(W\), and \(L\) into the formula and solve for \(m\). The highest fringe order can be obtained by rounding off the result to the nearest lower integer.
05

Solve for the case (b)

Repeat Step 4, but this time using \(d_b\) as the slit spacing.

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