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Problem 24 Medium Difficulty

Photons with a wavelength of 589 $\mathrm{nm}$ in air enter a plate of crown glass with index of refraction $n=1.52 .$ Find the (a) speed, (b) wavelength, and (c) energy of a photon in the glass.

Answer

a. $\text { The speed of a photon in crown glass is } 1.97 \times 10^{8} \mathrm{m} / \mathrm{s}$
b. $\text { The wavelength of light in crown glass is } 388 \mathrm{nm}$
c. $\text { The energy of a photon in crown glass is } 3.2 \text { eV. }$

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Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

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Zachary M.

Hope College

Video Transcript

Our question says that we have a photo on of wavelength 589 nano meters and air that enters a crown glass with an index of refraction in equal the 1.52 and it wants us to find the speed, wavelength and energy of the full time in the glass. So for part A to find this speed, we can use the fact that the index of refraction is defined as the speed of light in a vacuum, which is three times 10 of the eight meters per second, divided by the ah velocity, which that light is travelling in the glass. So if we saw for the Velocity V, we find that it's equal to the speed of light divided by the index of refraction planking those values. In this expression, we find that this is equal to one 0.97 times 10 88 in the unit ear are, uh, units of velocity, which is meters per second weaken. Box it in as your solution. For part a part B asked us to find the wavelength of the photonic glass without wavelength. We'll call it Lambda Prime is going to be equal to the wavelength of the photon and air divided by the index of refraction in the glass. In plugging those values and for this expression we find that this is 387.5 or 388 and the units here that we were using our nano meters and M, which is 10 to the minus nine meters. We can just leave in unit to Nana leaders, never part see were asked to find the energy of this photo on. Well, energy is equal to HC over Lambda, right? But the Lambda value that we want to use here is Lambda Prime. So for Lambda Prime, we use 388 nano meters. But you need to use the meter's version of that. So it's 388 times 10 to the minus nine meters. H year is planks constant at 6.63 times 10 to the minus 34 jewels. Time second, you can look up planks constant. You need thio and see here, of course, is the unit, huh? Ah, the speed of light. So this is five 0.13 times 10 to the minus 19. Jules, so 5.13 times 10 to the minus 19 jewels, which you could convert to electron volts. Just 3.2 electron volts. Lincoln Box set in as your solution for part C.

University of Kansas
Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Other Schools

Zachary M.

Hope College