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

Options

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

Explanation

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

### Step 1: Identify the focal lengths of the lenses
- The focal length of the convex lens (f1) is given as 40 cm.
- The focal length of the concave lens (f2) is given as 25 cm.

### Step 2: Convert the focal lengths from centimeters to meters
- Since power is measured in diopters (D), we need to convert the focal lengths into meters:
- f1 = 40 cm = 0.4 m
- f2 = 25 cm = 0.25 m

### Step 3: Determine the power of each lens
- The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where f is the focal length in meters.
- For the convex lens (P1):
\[ P1 = \frac{1}{f1} = \frac{1}{0.4} = 2.5 \, \text{D} \]
- For the concave lens (P2):
\[ P2 = \frac{1}{f2} = \frac{1}{-0.25} = -4 \, \text{D} \]
(Note: The focal length of the concave lens is negative.)

### Step 4: Calculate the total power of the combination
- The total power (P) of the combination of the lenses is the sum of the individual powers:
\[ P = P1 + P2 = 2.5 + (-4) = 2.5 - 4 = -1.5 \, \text{D} \]

### Conclusion
- The power of the combination of the convex lens and the concave lens is \(-1.5 \, \text{D}\).

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