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Chapter 3: Problem 23

What is the highest-order maximum for 400-nm light falling on double slits separated by \(25.0 \mu \mathrm{m}\) ?

Short Answer

Expert verified
The highest-order maximum for 400-nm light falling on double slits separated by \(25.0 \mu m\) is 62.

Step by step solution

01

Write the formula for the position of maxima in a double-slit interference pattern

The formula to calculate the position of maxima in a double-slit interference pattern is as follows: \(m\lambda = d\sin\theta\) where m represents the order of the maximum, λ is the wavelength of the light, d is the slit separation, and θ is the angle between the maximum and the central maximum.
02

Find the highest-order maximum

To find the highest-order maximum, we will rearrange the formula from step 1 to solve for m: \(m = \frac{d\sin\theta}{\lambda}\) The highest-order maximum occurs when the angle θ approaches 90°, which means that sin(θ) approaches 1. We can substitute the given values for λ and d into the formula for m: \(d = 25.0 \mu m = 25.0 \times 10^{-6} m\), \(\lambda = 400 nm = 400 \times 10^{-9} m\) \(m = \frac{(25.0 \times 10^{-6})(1)}{(400 \times 10^{-9})}\) Calculating the value of m: \(m = \frac{25.0 \times 10^{-6}}{400 \times 10^{-9}}\) \(m ≈ 62.5\) Since the order m must be an integer, the highest-order maximum is 62.

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Most popular questions from this chapter

Monochromatic light of frequency \(5.5 \times 10^{14} \mathrm{Hz}\) falls on 10 slits separated by \(0.020 \mathrm{mm}\). What is the separation between the first and third maxima on a screen that is \(2.0 \mathrm{m}\) from the slits?

Fifty-one narrow slits are equally spaced and separated by \(0.10 \mathrm{mm}\). The slits are illuminated by blue light of wavelength \(400 \mathrm{nm} .\) What is angular position of the twenty-fifth secondary maximum? What is its peak intensity in comparison with that of the primary maximum?

A soap bubble is blown outdoors. What colors (indicate by wavelengths) of the reflected sunlight are seen enhanced? The soap bubble has index of refraction 1.36 and thickness 380 nm.

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