A ray of light is incident on a glass slab making an angle of `30^@` with the surface. The angle of refraction in glass, if the refractive index of flass is 1.6 , is

Options

A. `28^@`
B. `33^@`
C. `12^@`
D. `15^@`

Answer

To solve the problem of finding the angle of refraction in a glass slab when a ray of light is incident at an angle of \(30^\circ\) with the surface, we can use Snell's Law. Here’s a step-by-step solution:

### Step 1: Understand the given information
- The angle of incidence \(i\) is given as \(30^\circ\).
- The refractive index of air (\(\mu_1\)) is approximately 1 (since air is the first medium).
- The refractive index of glass (\(\mu_2\)) is given as 1.6.

### Step 2: Convert the angle of incidence
Since the angle of incidence is given with respect to the surface, we need to convert it to the angle with respect to the normal. The angle of incidence \(i\) with respect to the normal is:
\[ i = 90^\circ - 30^\circ = 60^\circ \]

### Step 3: Apply Snell's Law
Snell's Law states:
\[ \mu_1 \sin(i) = \mu_2 \sin(r) \]
Where:
- \(i\) is the angle of incidence,
- \(r\) is the angle of refraction.

Substituting the known values:
\[ 1 \cdot \sin(60^\circ) = 1.6 \cdot \sin(r) \]

### Step 4: Calculate \(\sin(60^\circ)\)
From trigonometry, we know:
\[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866 \]

### Step 5: Substitute and solve for \(\sin(r)\)
Now, substituting \(\sin(60^\circ)\) into the equation:
\[ 0.866 = 1.6 \cdot \sin(r) \]
To find \(\sin(r)\), we rearrange the equation:
\[ \sin(r) = \frac{0.866}{1.6} \approx 0.54125 \]

### Step 6: Find the angle of refraction \(r\)
Now, we take the inverse sine to find \(r\):
\[ r = \sin^{-1}(0.54125) \approx 32.7^\circ \]

### Final Answer
The angle of refraction in the glass slab is approximately \(32.7^\circ\).

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