To a fish in an aquarium, the 4.00mm-thick walls appear to be only 3.50mmthick. What is the index of refraction of the walls?

Short Answer

Expert verified

The index of refraction of the walls is1.52

Step by step solution

01

By given data.

To find the refractive index of the aquarium walls, use the equation that shows the relationship between the refractive indices of the two media, the real thickness, and the apparent thickness.

02

Deriving the equation for the refractive index of the aquarium

The relationship between the wall's true thickness Sand its apparent thickness sis given by,

s=nwnaqs

The refractive index of water is nw, and the refractive index of aquarium walls is naq.

Rearrange the equation for the aquarium's refractive index.

naq=ssnw

03

To find the refraction of the walls

The refractive index of the aquarium's walls is,

naq=ssnw

Substituting 4.00mmfor S, 3.50mmfor s, and 1.33for nw.

role="math" localid="1651391770543" naq=4.00mm3.50mm1.33

=1.52

As a result, the aquarium's walls have a refraction index of1.52

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