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Chapter 34: Problem 18

A red laser pointer is shined on a diffraction grating, producing a diffraction pattern on a screen behind the diffraction grating. If the red laser pointer is replaced with a green laser pointer, will the green bright spots on the screen be closer together or farther apart than the red bright spots were?

Short Answer

Expert verified
Answer: The green bright spots in a diffraction pattern are closer together than the red bright spots. This is due to the shorter wavelength of green light, which results in a more compact diffraction pattern as the bright spots are closer to the central maximum.

Step by step solution

01

Understand the concept of diffraction grating

A diffraction grating is a device that diffracts light into its constituent wavelengths. It usually consists of a surface with multiple parallel slits, which allow light waves to interfere with each other, creating a diffraction pattern on a screen behind the grating. The distance between the bright spots in the diffraction pattern depends on the wavelength of the light and the properties of the grating.
02

Determine the formula for calculating the angle of diffraction

To analyze the diffraction patterns created by the red and green laser pointers, we can use the formula for calculating the angle of diffraction (θ) in a diffraction grating: \(theta = sin^{–1}\left(\dfrac{m\lambda}{d}\right)\) where \(m\) is an integer representing the diffraction order, \(\lambda\) is the wavelength of the light, and \(d\) is the distance between adjacent slits on the grating. This formula is derived from the condition for constructive interference, which states that the bright spots in a diffraction pattern are formed when the path difference between adjacent slits is an integer multiple of the wavelength.
03

Compare red and green light wavelengths

Red light has a longer wavelength than green light. Typically, red light has a wavelength of about 650 nm, while green light has a wavelength of about 532 nm. To compare the diffraction patterns formed by the two colors of light, we can plug their respective wavelengths into the formula for the angle of diffraction: θ_red = sin^(-1)((m * 650 nm) / d) θ_green = sin^(-1)((m * 532 nm) / d)
04

Compare the angles of diffraction for red and green light

From the previous step, we can see that the angle of diffraction for green light is smaller than the angle of diffraction for red light for the same diffraction order (m) and distance between slits (d). This means that the green bright spots in the diffraction pattern formed by the green laser pointer will be closer to the central maximum (which corresponds to m = 0) than the red bright spots formed by the red laser pointer.
05

Conclude whether green bright spots are closer together or farther apart

Since the angles of diffraction for green light are smaller than the angles of diffraction for red light, the green bright spots in the diffraction pattern will be closer together than the red bright spots. This is because green light has a shorter wavelength, which results in a more compact diffraction pattern as the bright spots are closer to the central maximum.

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Most popular questions from this chapter

In a double-slit experiment, He-Ne laser light of wavelength \(633 \mathrm{nm}\) produced an interference pattern on a screen placed at some distance from the slits. When one of the slits was covered with a thin glass slide of thickness \(12.0 \mu \mathrm{m},\) the central fringe shifted to the point occupied earlier by the 10 th dark fringe (see figure). What is the refractive index of the glass slide? (a) Without the glass slide (b) With glass slide

For a double-slit experiment, two 1.50 -mm wide slits are separated by a distance of \(1.00 \mathrm{~mm} .\) The slits are illuminated by a laser beam with wavelength \(633 \mathrm{nm} .\) If a screen is placed \(5.00 \mathrm{~m}\) away from the slits, determine the separation of the bright fringes on the screen.

A glass with a refractive index of 1.50 is inserted into one arm of a Michelson interferometer that uses a 600.-nm light source. This causes the fringe pattern to shift by exactly 1000 fringes. How thick is the glass?

Which of the following light types on a grating with 1000 rulings with a spacing of \(2.00 \mu \mathrm{m}\) would produce the largest number of maxima on a screen \(5.00 \mathrm{~m}\) away? a) blue light of wavelength \(450 \mathrm{nm}\) b) green light of wavelength \(550 \mathrm{nm}\) c) yellow light of wavelength \(575 \mathrm{nm}\) d) red light of wavelength \(625 \mathrm{nm}\) e) need more information

How many lines per centimeter must a grating have if there is to be no second- order spectrum for any visible wavelength \((400-750 \mathrm{nm})\) ?
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