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Chapter 4: Problem 9

Is higher resolution obtained in a microscope with red or blue light? Explain your answer.

Short Answer

Expert verified
Higher resolution is obtained in a microscope with blue light. This is because blue light has a shorter wavelength (around 400nm) compared to red light (around 700nm). According to the Rayleigh criterion, the resolution of a microscope is directly proportional to the wavelength of light used. As a result, a shorter wavelength, like that of blue light, leads to a higher resolution.

Step by step solution

01

Understanding Wavelength and Color

The colors of light are determined by their wavelengths. Red light has a longer wavelength, typically around 700 nm, while blue light has a shorter wavelength, around 400 nm. So, red light has a larger wavelength value compared to blue light.
02

Understanding Resolution

Resolution is the ability of a microscope to distinguish two closely spaced objects as separate. In general, a smaller value for resolution indicates better (higher) resolution because it enables us to distinguish closely spaced objects more efficiently.
03

Relationship Between Wavelength and Resolution

The resolution of an optical instrument like a microscope depends on the wavelength of light used. According to the Rayleigh criterion, the resolution (R) of a microscope can be determined using the following formula: \[R = \dfrac{1.22 \lambda}{2NA}\] where: - R is the resolution - λ (lambda) is the wavelength of light used - NA is the numerical aperture of the microscope objective From the formula above, it can be observed that the resolution is directly proportional to the wavelength of light used. As the wavelength increases, the value of resolution increases, which in turn decreases the microscope's resolution.
04

Comparing Red and Blue Light Microscope Resolution

Since red light has a longer wavelength compared to blue light, using the formula above, we can deduce that using red light would result in a lower resolution in the microscope compared to using blue light. Therefore, higher resolution is obtained in a microscope with blue light.

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Most popular questions from this chapter

A single slit of width \(2100 \mathrm{nm}\) is illuminated normally by a wave of wavelength 632.8 nm. Find the phase difference between waves from the top and one third from the bottom of the slit to a point on a screen at a horizontal distance of \(2.0 \mathrm{m}\) and vertical distance of \(10.0 \mathrm{cm}\) from the center.

A diffraction grating with 2000 lines per centimeter is used to measure the wavelengths emitted by a hydrogen gas discharge tube. (a) At what angles will you find the maxima of the two first-order blue lines of wavelengths 410 and \(434 \mathrm{nm} ?\) (b) The maxima of two other first-order lines are found at \(\theta_{1}=0.097 \mathrm{rad}\) and \(\theta_{2}=0.132 \mathrm{rad} .\) What are the wavelengths of these lines?

The first-order Bragg angle for a certain crystal is \(12.1^{\circ} .\) What is the second-order angle?

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Microwaves of wavelength 10.0 mm fall normally on a metal plate that contains a slit \(25 \mathrm{mm}\) wide. (a) Where are the first minima of the diffraction pattern? (b) Would there be minima if the wavelength were \(30.0 \mathrm{mm}\) ?
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