A convex lens of focal length 40 cm a concave lens of focal length 40 and a concave lens of focal length 15 cm are placed in contact. The power of this combination of are placed in contact. The power of this combination in diopters is

Options

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

Explanation

To find the power of the combination of the lenses, we can follow these steps:

### Step 1: Identify the Focal Lengths
We have three lenses:
1. Convex lens (F1) with focal length \( f_1 = +40 \) cm
2. Concave lens (F2) with focal length \( f_2 = -40 \) cm
3. Concave lens (F3) with focal length \( f_3 = -15 \) cm

### Step 2: Convert Focal Lengths to Meters
Since power is measured in diopters (D), we need to convert the focal lengths from centimeters to meters:
- \( f_1 = 40 \) cm = \( 0.40 \) m
- \( f_2 = -40 \) cm = \( -0.40 \) m
- \( f_3 = -15 \) cm = \( -0.15 \) 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.

Calculating the power for each lens:
- For lens 1 (convex):
\[ P_1 = \frac{1}{0.40} = 2.5 \, \text{D} \]
- For lens 2 (concave):
\[ P_2 = \frac{1}{-0.40} = -2.5 \, \text{D} \]
- For lens 3 (concave):
\[ P_3 = \frac{1}{-0.15} \approx -6.67 \, \text{D} \]

### Step 4: Calculate the Total Power of the Combination
The total power \( P_{total} \) of the combination of lenses in contact is the sum of the individual powers:
\[ P_{total} = P_1 + P_2 + P_3 \]
Substituting the values:
\[ P_{total} = 2.5 + (-2.5) + (-6.67) = 2.5 - 2.5 - 6.67 = -6.67 \, \text{D} \]

### Final Answer
The power of the combination of the lenses is approximately:
\[ P_{total} \approx -6.67 \, \text{D} \]

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