The critical angle for glass to air refraction is least for which color ?

Options

A. Orange
B. Blue
C. Violet
D. Red

Answer

To determine the color for which the critical angle for glass-to-air refraction is least, we can follow these steps:

### Step 1: Understand the Concept of Critical Angle
The critical angle (ic) is defined as the angle of incidence at which light is refracted at an angle of 90 degrees in the second medium (in this case, air). It occurs when light travels from a denser medium (glass) to a less dense medium (air).

### Step 2: Apply Snell's Law
According to Snell's Law:
\[ \mu_1 \sin(i) = \mu_2 \sin(r) \]
Where:
- \( \mu_1 \) is the refractive index of glass,
- \( \mu_2 \) is the refractive index of air (approximately 1),
- \( i \) is the angle of incidence,
- \( r \) is the angle of refraction.

At the critical angle, the angle of refraction \( r \) is 90 degrees. Therefore, we can rewrite Snell's Law for the critical angle:
\[ \mu \sin(ic) = 1 \cdot \sin(90^\circ) \]
Since \( \sin(90^\circ) = 1 \), we have:
\[ \mu \sin(ic) = 1 \]

### Step 3: Rearranging the Formula
From the equation above, we can derive:
\[ \sin(ic) = \frac{1}{\mu} \]
This shows that the critical angle is inversely proportional to the refractive index (\( \mu \)) of the medium.

### Step 4: Relate Refractive Index to Wavelength
The refractive index of a medium is also inversely proportional to the wavelength of light. This means:
- Longer wavelengths (like red light) have a lower refractive index,
- Shorter wavelengths (like violet light) have a higher refractive index.

### Step 5: Determine the Relationship
Since the critical angle is inversely proportional to the refractive index, and the refractive index is inversely proportional to the wavelength, we can conclude:
- A longer wavelength (like red) will result in a larger critical angle,
- A shorter wavelength (like violet) will result in a smaller critical angle.

### Step 6: Conclusion
Thus, the critical angle is least for the color with the shortest wavelength, which is violet. Therefore, the answer is:
**The critical angle for glass to air refraction is least for violet color.**