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A transparent solid cube of side 'a' has...

A transparent solid cube of side 'a' has refractive index 3/2. A point source of light is embedded in it at its centre. Find the minimum area of the surface of the cube which must be painted black so that the source is not visible from outside.

Text Solution

Verified by Experts

The correct Answer is:
`(6 pi a^(2))/(5)`
On each side a circle of radius d tan C is to be painted black.

Here `d = a//2 & sin C = 2//3 = 1//a`
Now the answer is, `6 xx pi (d tan C)^(2) = 6`
`xx pi (a^(2))/(4).(4)/(15)=(6pi a^(2))/(5)`
Extal Sol. On each side a circle of radius, `(a)/(2) tan C` is to be painted black

`sin c = (2)/(3)`, area `= 6 xx pi ((a)/(2)tan c)^(2) = (6 pi a^(2))/(5)`
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