Geometric and wave optics

A ray of light passes from air to a glass with index of refraction $n=1.55$, with angle of incidence $35^{\circ }$. Compute the angle of refraction.

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Light with wavelength in vacuum $\lambda =480\mathrm{nm}$ propagates in a glass with $n=1.50$. Compute the speed, the frequency and the wavelength of the light in the glass.

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Diamond has index of refraction $n=2.42$. Compute the critical angle for light that, from inside a diamond, strikes the interface with air.

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Looking almost vertically from above at the surface of a pond ($n=1.33$), a fish appears to be at a depth of $0.90\mathrm{m}$. Compute the actual depth of the fish.

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An object is placed at $10\mathrm{cm}$ from a concave mirror with focal length $f=15\mathrm{cm}$. Determine the position of the image and the magnification, and state whether the image is real or virtual.

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A convex mirror has a radius of curvature of magnitude $40\mathrm{cm}$. An object is $30\mathrm{cm}$ from the mirror. Determine the position of the image and the magnification.

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An object and a screen are $90\mathrm{cm}$ apart. A converging lens with $f=20\mathrm{cm}$ is moved between the two. In which positions of the lens does the image of the object form sharply on the screen? Compute the magnification in each position.

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An object $4.0\mathrm{cm}$ tall is placed at $20\mathrm{cm}$ from a diverging lens with $f=-20\mathrm{cm}$. Determine the position and the height of the image.

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In a Young experiment with light of wavelength $550\mathrm{nm}$ and a screen at $1.8\mathrm{m}$, the bright fringes are $3.3\mathrm{mm}$ apart from each other. Compute the distance between the slits.

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A slit $0.050\mathrm{mm}$ wide is illuminated perpendicularly with light of wavelength $600\mathrm{nm}$. Compute the angle at which the second diffraction minimum is observed and its distance from the center on a screen at $1.0\mathrm{m}$.

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A grating with $600$ lines per millimeter, illuminated perpendicularly, gives the first-order maximum at $20.0^{\circ }$ from the direction of incidence. Compute the wavelength of the light and the maximum observable order.

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Vertically polarized light, of intensity $50W/{\mathrm{m}}^2$, passes through a polarizer with its axis at $60^{\circ }$ from the vertical and then through a second polarizer with a horizontal axis. Compute the final intensity.

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Unpolarized light is incident from air on a glass plate with $n=1.50$. Compute the angle of incidence for which the reflected light is totally polarized and the corresponding angle of refraction.

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