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

Explanation

To find the power of the lens combination consisting 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
- Convert the focal lengths from centimeters to meters:
- F1 = 40 cm = 0.4 m
- F2 = -25 cm = -0.25 m

### Step 3: Use the Lens Formula
- The formula for the focal length (f) of a combination of two lenses in contact is given by:
\[ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \]
- Substitute the values of F1 and F2 into the formula:
\[ \frac{1}{f} = \frac{1}{0.4} + \frac{1}{-0.25} \]

### Step 4: Calculate the Individual Terms
- Calculate \(\frac{1}{0.4}\):
\[ \frac{1}{0.4} = 2.5 \]
- Calculate \(\frac{1}{-0.25}\):
\[ \frac{1}{-0.25} = -4 \]

### Step 5: Combine the Terms
- Now, combine the two results:
\[ \frac{1}{f} = 2.5 - 4 = -1.5 \]

### Step 6: Find the Focal Length of the Combination
- Take the reciprocal to find the focal length (f):
\[ f = \frac{1}{-1.5} = -\frac{2}{3} \text{ m} \approx -0.6667 \text{ m} \]

### Step 7: Calculate the Power of the Lens Combination
- The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \text{ (in meters)} \]
- Since we have \(\frac{1}{f} = -1.5\), the power is:
\[ P = -1.5 \text{ diopters} \]

### Final Answer
The power of the lens combination is \(-1.5\) diopters.

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