Question

A person looking into an empty container is able to see the far edge of the container's bottom as shown in Figure (a). The height of the container is $h$, and its width is $d$. When the container is completely filled with a fluid of index of refraction $n$ and viewed from the same angle, the person can see the center of a coin at the middle of the container's bottom as shown in the Figure (b). (a) Show that the ratio $h/d$ is given by $frac{h}{d} = sqrt{frac{n^{2} - 1}{4 - n^{2}}}$ (Do this on paper. Your instructor may ask you to turn in this work.) (b) Assuming the container has a width of 1.48 cm and is filled with water, use the expression above to find the height of the container. cm (c) For what range of values of $n$ will the center of the coin not be visible for any values of $h$ and $d$? $n >$

          A person looking into an empty container is able to see the far edge of the container's bottom as shown in Figure (a). The height of the container is $h$, and its width is $d$. When the container is completely filled with a fluid of index of refraction $n$ and viewed from the same angle, the person can see the center of a coin at the middle of the container's bottom as shown in the Figure (b).
(a) Show that the ratio $h/d$ is given by
$frac{h}{d} = sqrt{frac{n^{2} - 1}{4 - n^{2}}}$
(Do this on paper. Your instructor may ask you to turn in this work.)
(b) Assuming the container has a width of 1.48 cm and is filled with water, use the expression above to find the height of the container.
____ cm
(c) For what range of values of $n$ will the center of the coin not be visible for any values of $h$ and $d$?
$n >$ ____

$A person looking into an empty container is able to see the far edge of the container's bottom as shown in Figure (a). The height of the container is h, and its width is d. When the container is completely filled with a fluid of index of refraction n and viewed from the same angle, the person can see the center of a coin at the middle of the container's bottom as shown in the Figure (b). (a) Show that the ratio h/d is given by frachd = sqrtfracn^2 - 14 - n^2 (Do this on paper. Your instructor may ask you to turn in this work.) (b) Assuming the container has a width of 1.48 cm and is filled with water, use the expression above to find the height of the container. cm (c) For what range of values of n will the center of the coin not be visible for any values of h and d? n >$

Added by Casey C.

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