All the listed things below are made of flint glass. Which one of these have greatest dispersive power (`omega`).

Options

A. prism
B. glass slab
C. biconvex lens
D. all have same `omega`

Explanation

To solve the question regarding which item made of flint glass has the greatest dispersive power (denoted as ω), we can follow these steps:

### Step 1: Understand Dispersive Power
Dispersive power (ω) is defined as the ratio of angular dispersion to the mean deviation. Mathematically, it can be expressed as:
\[ \omega = \frac{\text{Angular Dispersion}}{\text{Mean Deviation}} \]

### Step 2: Define Angular Dispersion
Angular dispersion can be defined in terms of the refractive indices for violet (μv) and red (μr) light:
\[ \text{Angular Dispersion} = \text{Deviation due to Violet} - \text{Deviation due to Red} \]
This can be expressed as:
\[ \text{Angular Dispersion} = (\mu_v - 1) \cdot A - (\mu_r - 1) \cdot A \]
Where A is the angle of the prism.

### Step 3: Simplify Angular Dispersion
From the above expression, we can simplify the angular dispersion:
\[ \text{Angular Dispersion} = A \cdot (\mu_v - \mu_r) \]

### Step 4: Define Mean Deviation
The mean deviation (Δm) can be defined as:
\[ \text{Mean Deviation} = (\mu_m - 1) \cdot A \]
Where μm is the mean refractive index for the spectrum.

### Step 5: Combine the Expressions
Now, substituting the expressions for angular dispersion and mean deviation into the formula for dispersive power:
\[ \omega = \frac{A \cdot (\mu_v - \mu_r)}{(\mu_m - 1) \cdot A} \]
The angle A cancels out, leading to:
\[ \omega = \frac{\mu_v - \mu_r}{\mu_m - 1} \]

### Step 6: Analyze the Material
Since all items are made of the same material (flint glass), the values of μv, μr, and μm will be the same for all items. Therefore, the dispersive power (ω) will also be the same for all items.

### Conclusion
Since the dispersive power depends only on the material and not on the shape or size of the items, we conclude that all items made of flint glass have the same dispersive power. Thus, the answer is that all options have the same dispersive power.

### Final Answer
**All items made of flint glass have the same dispersive power (ω).**

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