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Chapter 25: Problem 50

The diffraction pattern from a single slit is viewed on a screen. Using blue light, the width of the central maximum is \(2.0 \mathrm{cm} .\) (a) Would the central maximum be narrower or wider if red light is used instead? (b) If the blue light has wavelength \(0.43 \mu \mathrm{m}\) and the red light has wavelength \(0.70 \mu \mathrm{m},\) what is the width of the central maximum when red light is used?

Short Answer

Expert verified
Answer: The width of the central maximum when red light is used will be approximately 3.3 cm.

Step by step solution

01

Compare Wavelengths of Blue and Red Light

Blue light has a shorter wavelength than red light, which means that blue light diffracts less than red light. As a result, red light will create a wider central maximum than blue light.
02

Find the Ratio of the Wavelengths and Obtain the Width of the Central Maximum

To determine the width of the central maximum when red light is used, we'll first find the wavelength ratio: \(\frac{\lambda_{red}}{\lambda_{blue}} = \frac{0.70}{0.43}\). Now to find the width of the central maximum with red light, multiply the width of the central maximum with blue light by the ratio of the wavelengths: \(width_{red} = width_{blue} \times \frac{\lambda_{red}}{\lambda_{blue}}\). Using the given values: \(width_{red} = 2.0 \mathrm{cm} \times \frac{0.70}{0.43} \approx 3.3 \mathrm{cm}\). So, the width of the central maximum when red light is used is approximately 3.3 cm.

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