Three prisms 1, 2 and 3 have the prism angle `A = 60^(@)`, but their refractive indices are respectively 1.4, 1.5 and 1.6. If `delta_(1), delta_(2), delta_(3)` be their respective angles of deviation then

Options

A. `delta_(3) gt delta_(2) gt delta_(1)`
B. `delta_(1) gt delta_(2) gt delta_(3)`
C. `delta_(1) = delta_(2) = delta_(3)`
D. `delta_(2) gt delta_(1) gt delta_(3)`

Answer

To solve the problem, we need to find the angles of deviation (\( \delta_1, \delta_2, \delta_3 \)) for the three prisms with the same prism angle \( A = 60^\circ \) but different refractive indices (\( \mu_1 = 1.4, \mu_2 = 1.5, \mu_3 = 1.6 \)).

### Step-by-step Solution:

1. **Understanding the Relationship**:
The angle of deviation \( \delta \) for a prism is given by the formula:
\[ \delta = (\mu - 1) \cdot A \]
where \( \mu \) is the refractive index and \( A \) is the prism angle.

2. **Substituting the Values**:
Since all three prisms have the same angle \( A = 60^\circ \), we can calculate the angles of deviation for each prism:
- For Prism 1:
\[ \delta_1 = (1.4 - 1) \cdot 60^\circ = 0.4 \cdot 60^\circ = 24^\circ \]
- For Prism 2:
\[ \delta_2 = (1.5 - 1) \cdot 60^\circ = 0.5 \cdot 60^\circ = 30^\circ \]
- For Prism 3:
\[ \delta_3 = (1.6 - 1) \cdot 60^\circ = 0.6 \cdot 60^\circ = 36^\circ \]

3. **Comparing the Angles of Deviation**:
Now we can compare the angles of deviation:
\[ \delta_1 = 24^\circ, \quad \delta_2 = 30^\circ, \quad \delta_3 = 36^\circ \]
From this, we can see that:
\[ \delta_3 > \delta_2 > \delta_1 \]

4. **Conclusion**:
Therefore, the angles of deviation for the three prisms are:
\[ \delta_1 < \delta_2 < \delta_3 \]

### Final Result:
- \( \delta_1 = 24^\circ \)
- \( \delta_2 = 30^\circ \)
- \( \delta_3 = 36^\circ \)