A coating is applied to a lens to minimize reflections. The index of refraction of the coating is $1.55$, and that of the lens is 1.48. If the coating is $177.4 \mathrm{~nm}$ thick, what wavelength is minimally reflected for normal incidence in the lowest order?

Refer to earlier exercise, assume that the coating eliminates the reflection of light of wavelength 550 nm at normal incidence. By what percentages is reflection diminished by the coating at $450 \mathrm{~nm}$?

Determine the minimum thickness of a soap film ( $n=$ 1.330) that will result in constructive interference of (a) the red $\mathrm{H}_\alpha$ line ( $\lambda=656.3 \mathrm{~nm}$ );

(II) A planoconvex lucite lens $3.4 \mathrm{~cm}$ in diameter is placed on a flat piece of glass as in Fig. 34-18. When $580-\mathrm{nm}$ light is incident normally, 44 bright rings are observed, the last one right at the edge. What is the radius of curvature of the lens surface, and the focal length of the lens? [Hint: see Problem 33.]

In our discussion of thin-film interference, we looked at light reflecting from a thin film. Consider one light ray, the direct ray, that transmits through the film without reflecting. Then consider a second ray, the reflected ray, that transmits through the first surface, reflects back to the second, reflects again from the first, and then transmits out into the air, parallel to the direct ray. For normal incidence, how thick must the film be, in terms of the wavelength of the light, for the outgoing rays to interfere destructively? Is it the same thickness as for reflected destructive interference?

In our discussion of thin-film interference, we looked at light reflecting from a thin film. What If? Consider one light ray, the direct ray, which transmits through the film without reflecting. Consider a second ray, the reflected ray, that transmits through the first surface, reflects from the second, reflects again from the first, and then transmits out into the air, parallel to the direct ray. For normal incidence, how thick must the film be, in terms of the wavelength of light, for the outgoing rays to interfere destructively? Is it the same thickness as for reflected

(II) A total of 31 bright and 31 dark Newton's rings (not counting the dark spot at the center) are observed when 560 -nm light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 34-18). How much thicker is the center than the edges?

A thin film of glass ( $n=1.50$ ) floats on a liquid of $n=1.35$ and is illuminated by light of $\lambda=580 \mathrm{~nm}$ incident from air above it. Find the minimum thickness of the glass, other than zero, that will produce destructive interference in the reflected light.

A lens appears greenish yellow ( $\lambda=570 \mathrm{~nm}$ is strongest) when white light reflects from it. What minimum thickness of coating $(n=1.25)$ do you think is used on such a glass lens $(n=1.56)$, and why?

A lens appears greenish yellow ($\lambda$ = 570 nm is strongest) when white light reflects from it. What minimum thickness of coating $(n = 1.25)$ do you think is used on such a (glass) lens, and why?

Suppose that one slit of a double-slit apparatus is wider than the other so that the intensity of light passing through it is twice as great. Determine the intensity $I$ as a function of position $(\theta)$ on the screen for coherent light.

A type of mirage called a pingo is often observed in Alaska. Pingos occur when the light from a small hill passes to an observer by a path that takes the light over a body of water warmer than the air. What is seen is the hill and an inverted image directly below it . Explain how these mirages are formed.

Determine the minimum thickness of a soap film ( $n=$ 1.330) that will result in constructive interference of (b) the blue $\mathrm{H}_\gamma$ line $(\lambda=434.0 \mathrm{~nm})$

A very thin sheet of plastic (n = 1.60) covers one slit of a double-slit apparatus illuminated by $540$-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?