A light ray is incident normally on one of the refracting faces of a prism and just emerges out grazing the second surface. Then, the relation between angle of the prism and its critical angle is

Options

A. A = C
B. `AneC`
C. `AltC`
D. `AgtC`

Answer

To solve the problem, we need to analyze the situation described in the question step by step.

### Step 1: Understand the Geometry of the Prism
We have a prism with an angle \( A \). A light ray is incident normally on one of the refracting faces of the prism. Since it is incident normally, the angle of incidence \( i_1 \) at this face is \( 0^\circ \).

### Step 2: Refraction at the First Face
When the light ray enters the prism, it will refract according to Snell's law. However, since it is incident normally, the angle of refraction \( r_1 \) will also be \( 0^\circ \). Thus, the light ray travels inside the prism without bending.

### Step 3: Emergence from the Second Face
The light ray will now reach the second face of the prism. As it travels through the prism, it will eventually reach the point where it just grazes the second surface. When a light ray grazes a surface, it means that the angle of refraction at that point is \( 90^\circ \).

### Step 4: Applying the Critical Angle Concept
The critical angle \( C \) is defined as the angle of incidence at which the angle of refraction is \( 90^\circ \). For the light ray to just graze the second surface, the angle of incidence \( i_2 \) at the second face must equal the critical angle \( C \).

### Step 5: Relating the Angles
From the geometry of the prism, we know that the angle of incidence \( i_2 \) at the second face can be expressed in terms of the angle of the prism \( A \) and the critical angle \( C \). Since the light ray travels through the prism, the relationship can be given as:
\[ i_2 + A = 90^\circ \]
Thus, we can express the critical angle as:
\[ C = 90^\circ - A \]

### Step 6: Final Relation
Since we have established that the angle of incidence at the second face is equal to the critical angle, we can set:
\[ C = A \]

Thus, the relation between the angle of the prism \( A \) and its critical angle \( C \) is:
\[ A = C \]

### Conclusion
The relation between the angle of the prism and its critical angle is:
\[ \text{Angle of the prism } A = \text{Critical angle } C \]