A container made of glass `(mu= 1.5)` contains a liquid. A ray of light passing through the liquid falls on the bottom of the container at an angle of incidence `theta= tan^(-1)""(0.9)` and completely polarized. The ray should strike the bottom of the container at an angle of incidences so that it undergoes total internal reflection

Options

A. `tan^(-1) (1.5)`
B. `sin^(-1) (0.9)`
C. `tan^(-1) (0.75)`
D. `sin^(-1) (0.45)`

Answer

To solve the problem step by step, we need to find the critical angle for total internal reflection in the glass container filled with a liquid. Here’s how we can approach the solution:

### Step 1: Understand the given parameters
- The refractive index of glass (μ) = 1.5
- The angle of incidence (θ) = tan^(-1)(0.9)

### Step 2: Calculate the angle of incidence (θ)
To find the angle of incidence θ, we can use the tangent function:
\[ \theta = \tan^{-1}(0.9) \]
Using a calculator, we find:
\[ \theta \approx 42.0^\circ \]

### Step 3: Determine the critical angle (C)
The critical angle for total internal reflection can be calculated using the formula:
\[ \sin C = \frac{1}{\mu} \]
Substituting the value of μ:
\[ \sin C = \frac{1}{1.5} = \frac{2}{3} \]

### Step 4: Calculate the critical angle (C)
Now, we find the critical angle C using the inverse sine function:
\[ C = \sin^{-1}\left(\frac{2}{3}\right) \]
Using a calculator, we find:
\[ C \approx 41.8^\circ \]

### Step 5: Conclusion
The ray should strike the bottom of the container at an angle of incidence greater than the critical angle (C) for total internal reflection to occur. Therefore, the angle of incidence must be greater than approximately 41.8°.

### Final Answer
The angle of incidence for total internal reflection should be greater than 41.8°.

---