A ray of light is incident on the glass prism at an angle of `40^(@)`. Find the angle of emergence, if the angle of prism is `60^(@)` and refractive index is 1.5.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
- Angle of incidence (i) = 40°
- Angle of prism (A) = 60°
- Refractive index (μ) = 1.5

### Step 2: Use Snell's Law to find the angle of refraction (r)
Using Snell's Law:
\[ \mu = \frac{\sin i}{\sin r} \]
We can rearrange this to find r:
\[ \sin r = \frac{\sin i}{\mu} \]
Substituting the values:
\[ \sin r = \frac{\sin 40°}{1.5} \]

### Step 3: Calculate the value of r
Now, we need to calculate \(\sin 40°\):
\[ \sin 40° \approx 0.6428 \]
Thus,
\[ \sin r = \frac{0.6428}{1.5} \approx 0.4285 \]
Now, we find r using the inverse sine function:
\[ r = \sin^{-1}(0.4285) \approx 25.5° \]

### Step 4: Find the angle of incidence for the second surface (i')
The angle of incidence on the second surface (i') can be found using:
\[ i' = A - r = 60° - 25.5° = 34.5° \]

### Step 5: Use Snell's Law again to find the angle of emergence (r')
Now, we apply Snell's Law again at the second interface:
\[ \mu = \frac{\sin i'}{\sin r'} \]
Rearranging gives:
\[ \sin r' = \mu \cdot \sin i' \]
Substituting the values:
\[ \sin r' = 1 \cdot \sin 34.5° \]
Calculating \(\sin 34.5°\):
\[ \sin 34.5° \approx 0.5660 \]
Thus,
\[ r' = \sin^{-1}(0.5660) \approx 34.5° \]

### Step 6: Conclusion
The angle of emergence (r') is approximately 34.5°.

### Summary of Steps
1. Identify given values.
2. Apply Snell's Law to find the angle of refraction (r).
3. Calculate the angle of incidence for the second surface (i').
4. Apply Snell's Law again to find the angle of emergence (r').