As temperature of medium increases the critical angle

Options

A. Increases
B. Decreases
C. Remains same
D. first increases then decreases

Answer

To solve the question regarding the effect of temperature on the critical angle, we can follow these steps:

### Step 1: Understand the Concept of Critical Angle
The critical angle is defined as the angle of incidence above which total internal reflection occurs when light travels from a denser medium to a rarer medium. It is denoted as \( \theta_c \) and is related to the refractive index \( \mu \) of the medium.

### Step 2: Recall the Relation for Critical Angle
The critical angle can be expressed using Snell's Law:
\[ \sin \theta_c = \frac{n_2}{n_1} \]
where \( n_1 \) is the refractive index of the denser medium and \( n_2 \) is the refractive index of the rarer medium (usually air, which has a refractive index of approximately 1). For a medium with refractive index \( \mu \):
\[ \sin \theta_c = \frac{1}{\mu} \]

### Step 3: Analyze the Effect of Temperature on Refractive Index
As the temperature of a medium increases, the medium typically becomes less dense (rarer). This decrease in density leads to a decrease in the refractive index \( \mu \).

### Step 4: Determine the Impact on Critical Angle
Since \( \sin \theta_c = \frac{1}{\mu} \), if \( \mu \) decreases due to an increase in temperature, then \( \sin \theta_c \) will increase. This implies that the critical angle \( \theta_c \) will also increase because the sine function is monotonically increasing in the range of angles from 0 to 90 degrees.

### Step 5: Conclusion
Thus, as the temperature of the medium increases, the critical angle increases.

### Final Answer
The critical angle will **increase** as the temperature of the medium increases.

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