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Light from an aquarium goes from water (n=43)through a plane of glass (n=32)into the air (n=1). Assuming its a monochromatic plane wave and that it strikes the glass at normal incidence, find the minimum and maximum transmission coefficients (Eq. 9.199). You can see the fish clearly; how well can it see you?

Short Answer

Expert verified

The minimum and maximum transmisssion coefficients are Tmin=0.93455andTmax=0.987959 respectively, and it is clearly seen that fish sees you just as well as you see it.

Step by step solution

01

Given information:

Given data:

The refractive index of water isn1=43.

The refractive index of glass isn2=32.

The refractive index of air isn3=1.

02

Determine the minimum and maximum transmission coefficients

Write the expression for the inversion of the transmission coefficient.

T-1=14n1n3[n1+n32+n12-n22n32-n22n22sin2n2ωdC]

Substitute n1=43, n2=32and n3=1in the above expression.

T-1=14431432+1+432-322r2-322322sin23ωd2CT-1=316499+1736×54×49sin23ωd2CT-1=4948+854836sin23ωd2C........(1)

For transmission coefficient to be minimum data-custom-editor="chemistry" sin23ωd2C=1.

Substitute data-custom-editor="chemistry" sin23ωd2C=1in equation (1).

data-custom-editor="chemistry" Tmin=4849+8536Tmin=0.93455

For transmission coefficient to be maximumdata-custom-editor="chemistry" sin23ωd2C=0.

Substitute data-custom-editor="chemistry" sin23ωd2C=0in equation (1).

Tmax=4849Tmax=0.987959

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