Question

The retardation of a uniaxial negative mineral of thickness 0.03 mm is 5160 nm in its principal section of indicatrix. If the refractive index corresponding to the E-ray is 1.486, the value of the refractive index (correct to three decimal places) of the O-ray is ........

Hint:

The retardation for uniaxial minerals can be calculated using the thickness, refractive indices, and wavelength. The refractive indices for the O-ray and E-ray can be determined from the formula provided.

Answer 1

Correct Answer: 1.658

Step 1: Use the formula for retardation.
The retardation \( R \) of a uniaxial negative mineral is related to the thickness of the mineral, the refractive indices of the E-ray and O-ray, and the wavelength of light. The formula is: \[ R = d \times (n_e - n_o) \] Where: - \( R \) is the retardation (5160 nm), - \( d \) is the thickness of the mineral (0.03 mm = 30,000 nm), - \( n_e \) is the refractive index of the E-ray (1.486), - \( n_o \) is the refractive index of the O-ray (which we need to find).

Step 2: Rearrange the formula to solve for \( n_o \).
Rearranging the formula to solve for \( n_o \): \[ n_o = n_e - \frac{R}{d} \] Substitute the known values: \[ n_o = 1.486 - \frac{5160}{30000} = 1.486 - 0.172 = 1.314 \] Thus, the refractive index of the O-ray is 1.314.