The critical angle for total internal reflection is_________ when a ray of light travels from glass to water than when it travels from glass to air.

Options

A. equal
B. lesser
C. greater
D. none of these

Answer

To determine the relationship between the critical angles for total internal reflection when light travels from glass to water compared to when it travels from glass to air, we can follow these steps:

### Step 1: Understand the Concept of Critical Angle
The critical angle is the angle of incidence above which total internal reflection occurs. It depends on the refractive indices of the two media involved.

### Step 2: Write the Formula for Critical Angle
The formula for the critical angle (C) can be expressed as:
\[ \sin C = \frac{n_1}{n_2} \]
where \( n_1 \) is the refractive index of the first medium (glass) and \( n_2 \) is the refractive index of the second medium (water or air).

### Step 3: Identify the Refractive Indices
- The refractive index of glass (\( n_{glass} \)) is typically around 1.5.
- The refractive index of water (\( n_{water} \)) is approximately 1.33.
- The refractive index of air (\( n_{air} \)) is approximately 1.0.

### Step 4: Calculate Critical Angles
1. **For Glass to Water**:
\[ \sin C_{GW} = \frac{n_{glass}}{n_{water}} = \frac{1.5}{1.33} \]
This gives us a critical angle \( C_{GW} \).

2. **For Glass to Air**:
\[ \sin C_{GA} = \frac{n_{glass}}{n_{air}} = \frac{1.5}{1.0} \]
This gives us a critical angle \( C_{GA} \).

### Step 5: Compare the Critical Angles
Since the refractive index of water is greater than that of air, we can conclude:
- \( n_{water} < n_{air} \) implies that \( C_{GW} > C_{GA} \).

### Conclusion
Thus, the critical angle for total internal reflection is **greater** when a ray of light travels from glass to water than when it travels from glass to air.

### Final Answer
The critical angle for total internal reflection is **greater** when a ray of light travels from glass to water than when it travels from glass to air.

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