An eye specialist prescribes spectacles having combination of convex lens of focal length 40cm in contact with a concave lens of focal length 25cm. The power of this lens combination in diopters is

Options

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

Explanation

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

### Step 1: Identify the Focal Lengths
- 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 (negative because it is a concave lens).

### Step 2: Convert Focal Lengths to Meters
- Since power is calculated in diopters (D), we need to convert the focal lengths from centimeters to meters:
- F1 = 40 cm = 40/100 m = 0.4 m
- F2 = -25 cm = -25/100 m = -0.25 m

### Step 3: Calculate 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:
\[ P_1 = \frac{1}{0.4} = 2.5 \, \text{D} \]
- For the concave lens:
\[ P_2 = \frac{1}{-0.25} = -4 \, \text{D} \]

### Step 4: Calculate the Total Power of the Combination
- The total power of the lens combination (P_total) is the sum of the individual powers:
\[ P_{\text{total}} = P_1 + P_2 = 2.5 + (-4) = 2.5 - 4 = -1.5 \, \text{D} \]

### Step 5: Conclusion
- The power of the lens combination is -1.5 diopters.

### Final Answer
The power of the lens combination is -1.5 D.

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