At what angle to the horizon the sun be for is reflected rays from the surface of pond to be completely polarized (`mu` of water =1.33)

Options

A. `16^(@)56`
B. `26^(@)56`
C. `36^(@)56`
D. `46^(@)56`

Answer

To solve the problem of finding the angle at which the sun must be positioned for the reflected rays from the surface of a pond to be completely polarized, we will use Brewster's Law. Here are the steps to arrive at the solution:

### Step 1: Understand Brewster's Law
Brewster's Law states that the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection, is known as Brewster's angle (θ_B). This angle can be calculated using the refractive index (μ) of the medium.

### Step 2: Write the formula for Brewster's angle
The formula for Brewster's angle is given by:
\[ \theta_B = \tan^{-1}(\mu) \]
where μ is the refractive index of the medium.

### Step 3: Substitute the given value of μ
In this case, the refractive index of water is given as μ = 1.33. Therefore, we can substitute this value into the formula:
\[ \theta_B = \tan^{-1}(1.33) \]

### Step 4: Calculate Brewster's angle
Using a calculator, we find:
\[ \theta_B \approx 53.06^\circ \]

### Step 5: Determine the angle of the sun to the horizon
The angle of the sun above the horizon (θ_s) can be found using the relationship:
\[ \theta_s = 90^\circ - \theta_B \]
Substituting the value of θ_B:
\[ \theta_s = 90^\circ - 53.06^\circ \approx 36.94^\circ \]

### Step 6: Round the answer
Rounding to the nearest degree, we find:
\[ \theta_s \approx 37^\circ \]

### Final Answer
The angle to the horizon at which the sun must be positioned for the reflected rays from the surface of the pond to be completely polarized is approximately **37 degrees**.

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