A convex lens of focal length 40cm is in contact with a concave lens of focal length 25cm. The power of the combination is

Options

A. `-1.5` dioptres
B. `-6.5` dioptres
C. `+6.5` dioptres
D. `+6.67` dioptres

Explanation

To find the power of the combination of a convex lens and a concave lens in contact, we can follow these steps:

### Step 1: Understand the formula for the combination of lenses
The formula for the focal length \( f \) of a combination of two lenses in contact is given by:
\[ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \]
where \( f_1 \) is the focal length of the first lens and \( f_2 \) is the focal length of the second lens.

### Step 2: Identify the focal lengths
In this case:
- The focal length of the convex lens \( f_1 = +40 \, \text{cm} \) (positive because it is a convex lens).
- The focal length of the concave lens \( f_2 = -25 \, \text{cm} \) (negative because it is a concave lens).

### Step 3: Substitute the values into the formula
Now, substituting the values into the formula:
\[ \frac{1}{f} = \frac{1}{40} + \frac{1}{-25} \]

### Step 4: Calculate the individual terms
Calculating each term:
\[ \frac{1}{40} = 0.025 \quad \text{(in meters)} \]
\[ \frac{1}{-25} = -0.04 \quad \text{(in meters)} \]

### Step 5: Combine the terms
Now, combine the terms:
\[ \frac{1}{f} = 0.025 - 0.04 = -0.015 \]

### Step 6: Find the focal length \( f \)
To find \( f \):
\[ f = \frac{1}{-0.015} \approx -66.67 \, \text{cm} \]

### Step 7: Calculate the power of the combination
The power \( P \) of a lens is given by:
\[ P = \frac{1}{f} \quad \text{(in meters)} \]
Converting \( f \) to meters:
\[ f = -0.6667 \, \text{m} \]
Now, calculating the power:
\[ P = \frac{1}{-0.6667} \approx -1.5 \, \text{diopters} \]

### Conclusion
Thus, the power of the combination of the lenses is:
\[ \text{Power} = -1.5 \, \text{D} \]