The angle of incidence on the surface of a diamond of refractive index 2.4, if the angle between the reflected and refracted rays is 90° is

Options

A. `tan^(-1)(2.4)`
B. `2sin^(-1)(1/2.4)`
C. `tan^(-1)(1/2.4)`
D. `cos^(-1)(1/2.4)`

Explanation

To solve the problem of finding the angle of incidence on the surface of a diamond with a refractive index of 2.4, given that the angle between the reflected and refracted rays is 90°, we can follow these steps:

### Step-by-Step Solution:

**Step 1: Understand the relationship between the angles.**
When light strikes a surface, it can be reflected or refracted. The angle between the reflected ray and the refracted ray being 90° indicates that we are dealing with the polarizing angle (also known as Brewster's angle).

**Step 2: Use the formula for Brewster's angle.**
The polarizing angle (IP) can be calculated using the formula:
\[ \tan(IP) = n \]
where \( n \) is the refractive index of the medium (in this case, diamond).

**Step 3: Substitute the given refractive index.**
Given that the refractive index \( n \) of diamond is 2.4, we can substitute this value into the formula:
\[ \tan(IP) = 2.4 \]

**Step 4: Calculate the polarizing angle.**
To find the polarizing angle, we take the arctangent (inverse tangent) of the refractive index:
\[ IP = \tan^{-1}(2.4) \]

Using a calculator or trigonometric tables, we find:
\[ IP \approx 67.3° \]

**Step 5: Conclusion.**
Thus, the angle of incidence on the surface of the diamond, when the angle between the reflected and refracted rays is 90°, is approximately 67.3°.

### Final Answer:
The angle of incidence is approximately **67.3°**.

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