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dedylja [7]
3 years ago
13

A fish inside the water 12cm below the surface looking up through the water sees the outside world contained in a circular horiz

on. If the refractive index of water is 4/3 the radius of circle is​

Physics
1 answer:
serg [7]3 years ago
4 0

Answer:

13.6 cm

Explanation:

From Snell's law:

n₁ sin θ₁ = n₂ sin θ₂

In the air, n₁ = 1, and light from the horizon forms a 90° angle with the vertical, so sin θ₁ = sin 90° = 1.

Given n₂ = 4/3:

1 = 4/3 sin θ

sin θ = 3/4

If x is the radius of the circle, then sin θ is:

sin θ = x / √(x² + 12²)

sin θ = x / √(x² + 144)

Substituting:

3/4 = x / √(x² + 144)

9/16 = x² / (x² + 144)

9/16 x² + 81 = x²

81 = 7/16 x²

x ≈ 13.6

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Answer:

(a). The charge on the outer surface is −2.43 μC.

(b). The charge on the inner surface is 4.00 μC.

(c). The electric field outside the shell is 3.39\times10^{7}\ N/C

Explanation:

Given that,

Charge q₁ = -4.00 μC

Inner radius = 3.13 m

Outer radius = 4.13 cm

Net charge q₂ = -6.43 μC

We need to calculate the charge on the outer surface

Using formula of charge

q_{out}=q_{2}-q_{1}

q_{out}=-6.43-(-4.00)

q_{out}=-2.43\ \mu C

The charge on the inner surface is q.

q+(-2.43)=-6.43

q=-6.43+2.43= 4.00\ \mu C

We need to calculate the electric field outside the shell

Using formula of electric field

E=\dfrac{kq}{r^2}

Put the value into the formula

E=\dfrac{9\times10^{9}\times6.43\times10^{-6}}{(4.13\times10^{-2})^2}

E=33927618.73\ N/C

E=3.39\times10^{7}\ N/C

Hence, (a). The charge on the outer surface is −2.43 μC.

(b). The charge on the inner surface is 4.00 μC.

(c). The electric field outside the shell is 3.39\times10^{7}\ N/C

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