A prism `(mu=1.5)` has the refracting angle of `30^(@)` The deviation of a monochromatic ray incident normally on its one surface will be `(sin 48^(@) 36 = 0.75)`

Options

A. `18^@ 36^'`
B. `20^@ 30^(')`
C. `18^@`
D. `22^@1^(')`

Explanation

To solve the problem, we need to find the deviation of a monochromatic ray incident normally on one surface of a prism with a refracting angle of \(30^\circ\) and a refractive index (\(\mu\)) of \(1.5\).

### Step-by-Step Solution:

1. **Understanding the Prism and Ray Incident**:
- The prism has a refracting angle \(A = 30^\circ\).
- The ray of light is incident normally on one surface of the prism, which means the angle of incidence \(I = 0^\circ\) at that surface.

2. **Finding the Angle of Refraction**:
- Since the ray is incident normally, it passes straight through the first surface without bending. Therefore, the angle of refraction \(R\) at the first surface is also \(0^\circ\).

3. **Using the Geometry of the Prism**:
- The angle of the prism is given as \(A = 30^\circ\).
- The angle of refraction at the second surface can be found using the relationship in the prism:
\[ R + E = A \]
where \(E\) is the angle of emergence. Since \(R = 0^\circ\):
\[ 0^\circ + E = 30^\circ \implies E = 30^\circ \]

4. **Applying Snell's Law**:
- At the second surface, we apply Snell's Law:
\[ \mu_1 \sin I = \mu_2 \sin E \]
- Here, \(\mu_1 = 1.5\) (the refractive index of the prism), \(\mu_2 = 1\) (the refractive index of air), and \(I = 30^\circ\) (the angle of incidence at the second surface).
- Thus, we have:
\[ 1.5 \sin 30^\circ = 1 \sin E \]
- Since \(\sin 30^\circ = \frac{1}{2}\):
\[ 1.5 \cdot \frac{1}{2} = \sin E \implies \sin E = 0.75 \]

5. **Finding the Emergent Angle**:
- We know from the problem that \(\sin E = 0.75\) corresponds to \(E = 48^\circ 36'\) (given in the problem).

6. **Calculating the Deviation**:
- The deviation (\(\delta\)) is given by:
\[ \delta = E - I \]
- Since the angle of incidence \(I\) at the second surface is \(30^\circ\):
\[ \delta = 48^\circ 36' - 30^\circ = 18^\circ 36' \]

### Final Answer:
The deviation of the monochromatic ray is \(18^\circ 36'\).

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