Light in air is incident on a plastic plate at the Brewster angle. The angle of refraction is `35.0^(@)`
What is the index of refraction of the plastic plate ?

Options

A. `1.58`
B. `1.36`
C. `1.43`
D. `1.61`

Answer

To find the index of refraction of the plastic plate when light in air is incident at the Brewster angle, we can follow these steps:

### Step 1: Understand Brewster's Angle
Brewster's angle (Ip) is defined as the angle of incidence at which the reflected and refracted rays are perpendicular to each other. This means that if the angle of refraction is R', then the angle of reflection R will be such that:
\[ R + R' = 90^\circ \]

### Step 2: Use the Given Angle of Refraction
We are given that the angle of refraction (R') is \( 35^\circ \). Using the relationship from Step 1, we can find the angle of reflection (R):
\[ R = 90^\circ - R' = 90^\circ - 35^\circ = 55^\circ \]

### Step 3: Apply the Law of Reflection
According to the law of reflection, the angle of incidence (I) is equal to the angle of reflection (R):
\[ I = R \]
Thus, we have:
\[ I = 55^\circ \]

### Step 4: Relate Brewster's Angle to Refractive Index
The relationship between Brewster's angle and the refractive index (μ) is given by:
\[ \tan(I_p) = μ \]
Since we have found that the Brewster angle (Ip) is \( 55^\circ \), we can write:
\[ μ = \tan(55^\circ) \]

### Step 5: Calculate the Refractive Index
Now we need to calculate \( \tan(55^\circ) \):
Using a scientific calculator or trigonometric tables:
\[ \tan(55^\circ) \approx 1.428 \]

Thus, the index of refraction of the plastic plate is:
\[ μ \approx 1.428 \]

### Final Answer
The index of refraction of the plastic plate is approximately **1.428**.

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