# Thin Film#

Light of wavelength $$\lambda\_{\text{air}}$$ = 611 nm is incident (from the air, $$n\_{air} = 1.00$$) on a thin film of unknown index of refraction and thickness. The film is attached to a glass surface ($$n\_{\text{glass}} = 1.5$$). The path length difference traveled by the light reflecting from the front and back surfaces of the film corresponds to $$\frac{\lambda\_{\text{film}}}{2}$$ (half a wavelength). Light reflecting off both the front and back surfaces of the film experiences a $$\pi$$ rad (initial) phase shift.

## Part 1#

This implies that the reflected light from these two reflections will be;

• {â€˜valueâ€™: â€˜in phase causing constructive interference of the reflected light. â€˜}

• {â€˜valueâ€™: â€˜out of phase causing destructive interference of the reflected light. â€˜}

## Part 2#

What must the product of the film thickness and the filmâ€™s index of refraction be?

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## Part 3#

In order for both reflections to experience $$\pi$$ rad phase shifts, what range of values can $$n\_{\text{film}}$$ take?

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## #

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## Part 4#

What is the lower limit on how thick the film could be, given your answers to on the previous questions?

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## Part 5#

If the thin film had a thickness of 148nm, what index of refraction would the thin film have to have?

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## Part 6#

If the film thickness was now doubled, the reflected light from the front and back surfaces of the film would be;

• {â€˜valueâ€™: â€˜in phase causing constructive interference of the reflected light. â€˜}

• {â€˜valueâ€™: â€˜out of phase causing destructive interference of the reflected light. â€˜}

## Part 7#

If you were to design anti-reflective coatings for glasses with this thin film material and this color of light, which film thickness would you choose?