The velocity of light in a medium is half its velocity in air. If a ray of light emerges from such a medium into air, the angle of incidenc, at which it will be totally internally reflected, is

Options

A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Explanation

To solve the problem, we need to determine the angle of incidence at which total internal reflection occurs when light transitions from a medium to air. Here’s a step-by-step solution:

### Step 1: Understand the given information
We know that the velocity of light in the medium (Vm) is half of its velocity in air (C). Therefore, we can express this as:
\[ V_m = \frac{C}{2} \]

### Step 2: Calculate the refractive index (μ)
The refractive index (μ) of a medium is defined as the ratio of the speed of light in air (or vacuum) to the speed of light in the medium:
\[ \mu = \frac{C}{V_m} \]
Substituting the value of Vm:
\[ \mu = \frac{C}{\frac{C}{2}} = 2 \]

### Step 3: Determine the critical angle (C)
Total internal reflection occurs when the angle of incidence exceeds the critical angle (C). The critical angle can be found using the formula:
\[ \sin C = \frac{1}{\mu} \]
Substituting the value of μ:
\[ \sin C = \frac{1}{2} \]

### Step 4: Calculate the critical angle
Now, we can find the critical angle by taking the inverse sine:
\[ C = \sin^{-1}\left(\frac{1}{2}\right) \]
This gives us:
\[ C = 30^\circ \]

### Step 5: Conclusion
For total internal reflection to occur, the angle of incidence must be greater than the critical angle. Therefore, the angle of incidence at which total internal reflection will start is:
\[ \text{Angle of incidence} > 30^\circ \]

### Final Answer
The angle of incidence at which total internal reflection occurs is greater than 30 degrees.

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