The focal length of a thin convex lens for red and blue colours is 100.5 cm and 99.5 cm .The dispersive power of the lens is

Options

A. 0.01
B. 0.02
C. 1.005
D. 0.995

Explanation

To find the dispersive power of the lens, we will follow these steps:

### Step 1: Understand the formula for dispersive power
The dispersive power (Ω) of a lens is given by the formula:
\[ \Omega = \frac{f_{red} - f_{blue}}{f_{yellow}} \]
where:
- \( f_{red} \) is the focal length for red light,
- \( f_{blue} \) is the focal length for blue light,
- \( f_{yellow} \) is the focal length for yellow light.

### Step 2: Calculate the focal length for yellow light
The focal length for yellow light can be calculated using the formula:
\[ f_{yellow} = \sqrt{f_{red} \cdot f_{blue}} \]
Given:
- \( f_{red} = 100.5 \, \text{cm} \)
- \( f_{blue} = 99.5 \, \text{cm} \)

Substituting the values:
\[ f_{yellow} = \sqrt{100.5 \times 99.5} \]

### Step 3: Perform the calculation for \( f_{yellow} \)
Calculating \( f_{yellow} \):
\[ f_{yellow} = \sqrt{100.5 \times 99.5} = \sqrt{10000.25} \approx 100.00125 \, \text{cm} \]

### Step 4: Substitute the values into the dispersive power formula
Now we can substitute the values into the dispersive power formula:
\[ \Omega = \frac{100.5 - 99.5}{100.00125} \]

### Step 5: Perform the subtraction and division
Calculating the numerator:
\[ 100.5 - 99.5 = 1.0 \]

Now substituting this back into the dispersive power formula:
\[ \Omega = \frac{1.0}{100.00125} \approx 0.009999875 \]

### Step 6: Round the answer
Rounding to two decimal places, we get:
\[ \Omega \approx 0.01 \]

### Final Answer
The dispersive power of the lens is approximately \( 0.01 \).

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