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Chapter 32: Problem 18

Green light at \(520 \mathrm{nm}\) is diffracted by a grating with 3000 lines/cm. Through what angle is the light diffracted in (a) first and (b) fifth order?

Short Answer

Expert verified
The diffraction angles for the first and the fifth order are calculated by applying the formula for diffraction grating and adjusted appropriately. This illustrates how the diffraction angle varies according to the order of diffraction.

Step by step solution

01

Convert the Units

First, convert the grating spacing from lines per centimeter to lines per meter. As the grating has 3000 lines/cm, the total number of lines per meter will be 3000x10^4 lines/meter or 3x10^8 lines/meter. Therefore, the distance between the slits (d) is the reciprocal of the total lines per meter. So, \(d = 1/(3x10^8) = 3.33x10^{-9} m\). Convert the wavelength of the light from nanometers to meters. As there are 1x10^9 nm in 1 m, the wavelength (位) in meters is \(520x10^-9 m\).
02

Calculate the Diffraction Angles

Use the equation \(d\sin(\Theta)=m\lambda\) to find the diffraction angle for the first and the fifth orders. (a) For the first order (m=1), solve for \(\Theta\): \(\Theta_{1} = \arcsin(\lambda/(d*m)) = \arcsin((520x10^{-9})/(3.33x10^{-9}))\). (b) For the fifth order (m=5), again solve for \(\Theta\): \(\Theta_{5} = \arcsin(\lambda/(d*m)) = \arcsin((520x10^{-9})/(3.33x10^{-9}*5))\). Calculate these to find the respective angles.
03

Adjust the Angles

The calculator usually gives the angle in radians. Therefore, convert the angles from radians to degrees by multiplying by \(180/蟺\).

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Most popular questions from this chapter

A thin film of toluene \((n=1.49)\) floats on water. Find the minimum film thickness if the most strongly reflected light has wavelength \(460 \mathrm{nm}\).

An oil film with refractive index 1.25 floats on water. The film thickness varies from \(0.80 \mu \mathrm{m}\) to \(2.1 \mu \mathrm{m} .\) If 630 -nm light is incident normally on the film, at how many locations will it undergo enhanced reflection?

Light is incident on a diffraction grating at angle \(\alpha\) to the normal. Show that the condition for maximum light intensity becomes \(d(\sin \theta \pm \sin \alpha)=m \lambda\).

A tube of glowing gas emits light at \(550 \mathrm{nm}\) and \(400 \mathrm{nm} .\) In a double-slit apparatus, what's the lowest-order 550 -nm bright fringe that will fall on a 400 -nm dark fringe, and what are the fringes' corresponding orders?

On the screen of a multiple-slit system, the interference pattern shows bright maxima separated by \(0.86^{\circ}\) and seven minima between each bright maximum. (a) How many slits are there? (b) What's the slit separation if the incident light has wavelength \(656.3 \mathrm{nm} ?\)
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