You want to coat the inner surfaces of your windows (which have refractive index

Question

You want to coat the inner surfaces of your windows (which have refractive index of 1.51) with a film in order to enhance the reflection of light back into the room so that you can use bulbs of lower wattage than usual. You find that MgF2, with n = 1.38, is not too expensive, so you decide to use it. Since incandescent home lightbulbs emit reddish light with a peak wavelength of approximately 644 nm , you decide that this wavelength is the one to enhance in the light reflected back into the room.

A) What is the minimum thickness of film that you will need? t= ? nm

B) If this layer seems too thin to be able to put on accurately, what other thicknesses would also work? Give only the three thinnest ones nm

Explanation / Answer

A) condition for minimum thickness for constructive intereference

2*t = lamda/n

t = lamda/(2*n)

= 644 nm/(2*1.38)

= 2.33*10^-7 m

B) t2 = 2*lamda/(2*n)

= 2*2.33*10^-7

= 4.66*10^-7 m

t3 = 3*t

= 3*2.33*10^-7

= 6.99*10^-7 m

t4 = 4*t1

= 4*2.33*10^-7

= 9.32*10^-7 m

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