A beam of light is incident at the polarizing angle of `35^(@)` on a certain glass plate. The refractive index of the glass plate is:

Options

A. `sin 35^(@)`
B. `tan 35^(@)`
C. `tan 55^(@)`
D. `sin 55^(@)`

Explanation

To find the refractive index of the glass plate using the given polarizing angle, we can follow these steps:

### Step 1: Understand the relationship between the refractive index and the polarizing angle.
The refractive index (μ) of a medium can be calculated using the formula:
\[ \mu = \tan(I_p) \]
where \(I_p\) is the polarizing angle.

### Step 2: Identify the given polarizing angle.
From the question, we know that the polarizing angle \(I_p\) is given as \(35^\circ\).

### Step 3: Substitute the polarizing angle into the formula.
Now, we substitute \(I_p\) into the formula:
\[ \mu = \tan(35^\circ) \]

### Step 4: Calculate the value of \(\tan(35^\circ)\).
Using a scientific calculator or trigonometric tables, we find:
\[ \tan(35^\circ) \approx 0.7002 \]

### Step 5: State the refractive index.
Thus, the refractive index of the glass plate is:
\[ \mu \approx 0.7002 \]

### Final Answer:
The refractive index of the glass plate is approximately \(0.7002\).

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