Assume standard notations used for dispersion and deviation is a prise, in the following formulae:
(a) `del=del_(gamma)` (b) `del=(n_(gamma)-1)A`
( c) `theta=del_(v)-del_(R)` (d) `theta=(n_(V)-n_(R))A`
State which option(s) is / are correct.

Options

A. a and b are equivalent for a prism of small angle A, irrespective of I
B. The ratios of `theta//del` given by, using c and a, and using b and d, are same for a prism with small angle A, irrespective of I
C. b and d represent the most basic definitions of `theta` and `del` for a prism with small angle A, irrespective of I
D. a and c represent the most basic definitions of `theta` and `del` for a prism with small angle A, irrespective of :

Answer

To solve the problem, we need to analyze the given formulas and determine which options are correct based on the definitions of deviation and dispersion in the context of a prism.

### Step-by-Step Solution:

1. **Understanding the Formulas**:
- The formulas provided are:
- (a) \( \delta = \delta_y \)
- (b) \( \delta = (n_y - 1)A \)
- (c) \( \theta = \delta_v - \delta_r \)
- (d) \( \theta = (n_V - n_R)A \)

2. **Analyzing Formula (a)**:
- Formula (a) states that the total deviation \( \delta \) is equal to the deviation for yellow light \( \delta_y \).
- This is generally true for a specific wavelength but not universally applicable for all colors. Thus, this formula can be considered correct in the context of yellow light.

3. **Analyzing Formula (b)**:
- Formula (b) relates the deviation \( \delta \) to the refractive index \( n_y \) for yellow light and the angle of the prism \( A \).
- This is a standard formula derived from the principles of optics for a thin prism. Therefore, this formula is correct.

4. **Analyzing Formula (c)**:
- Formula (c) states that the angular dispersion \( \theta \) is equal to the difference in deviations for violet and red light.
- This is a correct representation of how dispersion is defined in optics, as it measures the spread of colors.

5. **Analyzing Formula (d)**:
- Formula (d) states that the angular dispersion \( \theta \) can also be expressed in terms of the refractive indices \( n_V \) and \( n_R \) for violet and red light respectively.
- This is also a valid expression for the angular dispersion in a prism.

6. **Conclusion**:
- All four formulas (a), (b), (c), and (d) are correct in the context of a prism's behavior with light of different wavelengths.

### Final Answer:
All options (a), (b), (c), and (d) are correct.