Question

The refractive indices of four minerals (P, Q, R, S) are as follows:
P (\( \alpha = 1.712 \), \( \beta = 1.721 \), \( \gamma = 1.727 \)),
Q (\( \epsilon = 1.553 \), \( \omega = 1.544 \)),
R (\( \alpha = 1.664 \), \( \beta = 1.672 \), \( \gamma = 1.694 \)),
S (\( \omega = 1.658 \), \( \epsilon = 1.486 \)).
The value of maximum birefringence among all the minerals is ......... (give answer in three decimal places).

Hint:

To calculate birefringence, subtract the minimum refractive index from the maximum refractive index for each mineral and compare the results.

Answer 1

Correct Answer: 0.172

Step 1: Understanding birefringence.
Birefringence is the difference in refractive indices between two principal refractive indices in a mineral. It is calculated as the difference between the maximum and minimum refractive indices for each mineral.
Step 2: Calculating birefringence for each mineral.
For each mineral, we calculate the birefringence by subtracting the minimum refractive index from the maximum refractive index:
- For P, the maximum refractive index is \( 1.727 \) and the minimum is \( 1.712 \). Birefringence = \( 1.727 - 1.712 = 0.015 \).
- For Q, the maximum refractive index is \( 1.553 \) and the minimum is \( 1.544 \). Birefringence = \( 1.553 - 1.544 = 0.009 \).
- For R, the maximum refractive index is \( 1.694 \) and the minimum is \( 1.664 \). Birefringence = \( 1.694 - 1.664 = 0.030 \).
- For S, the maximum refractive index is \( 1.658 \) and the minimum is \( 1.486 \). Birefringence = \( 1.658 - 1.486 = 0.172 \).
Step 3: Finding the maximum birefringence.
The maximum birefringence among all the minerals is \( 0.172 \) from mineral S.
Step 4: Conclusion.
Therefore, the maximum birefringence among all the minerals is 0.172.