Question

In: Physics

A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread...

A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread uniformly over the surface of crown glass of refractive index 1.52. Light of wavelength 490 nm falls at normal incidence onto the film from air. You want to increase the thickness of this film so that the reflected light cancels.

a) What is the minimum thickness of TiO2 that you must add so the reflected light cancels as desired?

b) After you make the adjustment in part (a), what is the path difference between the light reflected off the top of the film and the light that cancels it after traveling through the film? Express your answer in nanometers.

c) Express your answer in wavelengths of the light in the TiO2 film.

Solutions

Expert Solution

The condition for destructive interference of light reflected from the two surfaces of a thin film can be calculated using the thickness dd of the material, its refractive index nn and the wavelength λλ. This case is very common in antireflection coatings. If one assumes normal incidence, the condition for these coatings is

4nd=(2k+1)λ      k=1,2,3,...

In this configuration, we have the rare case that a coating with high refractive index nn is deposited at a substrate with lower refractive index. Therefore, we have to take into account a phase jump of λ/2λ/2 that the first reflected wave experiences and the second one doesn't. The second wave has a phase delay of 2nd2nd, where dd is the thickness of the layer. The difference between the two phases for destructive interference must be an odd multiple of half the wavelength. In mathematical notation, this reads

2nd−λ/2=(2k+1)λ/2

2nd=(2k+2)λ/2 (j=k+1)

d=jλn

=j⋅490 nm/(2.62)

=j⋅187.0 nm

The smallest integer yielding a thickness larger than the already existing 1036 nm is j = 6 resulting in a required thickness of 1122 nm.

A): A layer of thickness 86 nm has to be added to achieve destructive interference.

B): The path difference between the two waves is the difference of the optical path of the back reflection and the phase jump of the first reflection, i.e.

Δd=2 x 2.62 x 1122 nm−(460/2) nm = 5634.28 nm .

C): This corresponds to 11.5 wavelengths.


Related Solutions

A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread...
A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread uniformly over the surface of crown glass of refractive index 1.52. Light of wavelength 460 nm falls at normal incidence onto the film from air. You want to increase the thickness of this film so that the reflected light cancels. A) What is the minimum thickness of TiO2 that you must add so the reflected light cancels as desired? ΔT= ____ nm B) After...
A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread...
A uniform film of TiO2, 1036 nm thick and having index of refraction 2.62, is spread uniformly over the surface of crown glass of refractive index 1.52. Light of wavelength 450 nmfalls at normal incidence onto the film from air. You want to increase the thickness of this film so that the reflected light cancels. What is the minimum thickness of TiO2 that you must add so the reflected light cancels as desired? After you make the adjustment in part...
A 269 nm thin film with index of refraction 1.71 floats on water (with index of...
A 269 nm thin film with index of refraction 1.71 floats on water (with index of refraction 1.333). What is the largest wavelength of reflected light for which constructive interference occur? Answer in units of m (for this part I got 1.84 x 10 ^-6 m) I need help with the second part of the question: What is the 2nd largest wavelength that interferes constructively? Answer in units of m.
A thin film having an index of refraction of 1.50 is surrounded by air. It is...
A thin film having an index of refraction of 1.50 is surrounded by air. It is illuminated normally by white light. Analysis of the reflected light shows that the wavelengths 360, 450, and 600 nm are the only missing wavelengths in the visible portion of the spectrum. That is, for those wavelengths, there is destructive interference. (a) What is the thickness of the film? nm (b) What wavelengths in the visible portion of the spectrum are brightest in the reflected...
A thick lens has an index of refraction of 1.60. It is 4-cm thick and is...
A thick lens has an index of refraction of 1.60. It is 4-cm thick and is surrounded by air. The radius of curvature of the front surface is 5 cm, and the radius of curvature of the back surface is 12 cm. A 1-cm tall object is placed to the left of the first surface. At what angle above the optic axis should a ray strike the front side of the lens 0.5 cm above the optical axis so that...
A plastic film with index of refraction 1.85 is put on the surface of a car...
A plastic film with index of refraction 1.85 is put on the surface of a car window to increase the reflectivity and thus to keep the interior of the car cooler. The window glass has index of refraction 1.52. Part A What minimum thickness is required if light with wavelength 550 nm in air reflected from the two sides of the film is to interfere constructively? Part B It is found to be difficult to manufacture and install coatings as...
A glass window of index of refraction 1.3 is coated with an antireflective film of thickness...
A glass window of index of refraction 1.3 is coated with an antireflective film of thickness 2.0 µm. Which of the following indices of refraction of the film would cause the intensity of reflected light of wavelength 800 nm from a normally-incident beam to be suppressed? A. 1.1 B. 1.2 C. 1.4 D. 1.7 E. 1.8
A soap film (n=1.33) is 772 nm thick. White light strikes the film at normal incidence....
A soap film (n=1.33) is 772 nm thick. White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides? If there is more than one answer, separate them by a comma.
A lens is made of a transparent material having an index of refraction of 1.50. One...
A lens is made of a transparent material having an index of refraction of 1.50. One side of the lens is flat, and the other convex with a radius of curvature of 23.0 cm. (a) Find the focal length of the lens. (b) If an object is placed 110 cm in front of the lens, where will the image be located?
A thin uniform film of refractive index 1.750 is placed on a sheet of glass with...
A thin uniform film of refractive index 1.750 is placed on a sheet of glass with a refractive index 1.50. At room temperature ( 24.0o C), this film is just thick enough for light with a wavelength 582.9 nm reflected off the top of the film to be canceled by light reflected from the top of the glass. After the glass is placed in an oven and slowly heated to 164o C, you find that the film cancels reflected light...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT