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

Options

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

Explanation

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

### Step 1: Identify the Focal Lengths
- The focal length of the convex lens (f1) is +40 cm.
- The focal length of the concave lens (f2) is -25 cm (negative because it is a concave lens).

### Step 2: Use the Lens Formula
The formula for the combination of two lenses in contact is given by:
\[ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \]
Since the lenses are in contact, the distance (d) between them is 0, and thus we do not need to include it in our calculations.

### Step 3: Substitute the Values
Substituting the values of f1 and f2 into the formula:
\[ \frac{1}{f} = \frac{1}{40} + \frac{1}{-25} \]

### Step 4: Find a Common Denominator
To add the fractions, we find a common denominator. The least common multiple of 40 and 25 is 200. Thus:
\[ \frac{1}{40} = \frac{5}{200} \quad \text{and} \quad \frac{1}{-25} = \frac{-8}{200} \]
Now, substituting these values:
\[ \frac{1}{f} = \frac{5}{200} - \frac{8}{200} = \frac{-3}{200} \]

### Step 5: Solve for f
Taking the reciprocal to find the focal length (f):
\[ f = \frac{-200}{3} \text{ cm} \]

### Step 6: Convert Focal Length to Meters
To find the power in diopters, we need the focal length in meters. Convert cm to meters:
\[ f = \frac{-200}{3} \text{ cm} = \frac{-200}{3} \times \frac{1}{100} \text{ m} = \frac{-2}{3} \text{ m} \]

### Step 7: Calculate the Power
The power (P) of a lens is given by:
\[ P = \frac{1}{f} \text{ (in meters)} \]
Substituting the value of f:
\[ P = \frac{1}{\left(-\frac{2}{3}\right)} = -\frac{3}{2} \text{ diopters} = -1.5 \text{ diopters} \]

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

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