A convex lens of focal length 80 cm and a concave lens of focal length 50 cm are combined toghether. What will be their resulting power ?

Options

A. `+6.5 D`
B. `-6.5 D`
C. `+7.5 D`
D. `-0.75 D`

Answer

To find the resulting 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 80 cm.
- The focal length of the concave lens (f2) is given as 50 cm.

### 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:
- \( f_1 = 80 \, \text{cm} = 0.8 \, \text{m} \)
- \( f_2 = -50 \, \text{cm} = -0.5 \, \text{m} \) (negative because it is a concave lens)

### Step 3: Calculate the power of each lens
- The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
- For the convex lens:
\[ P_1 = \frac{1}{f_1} = \frac{1}{0.8} = 1.25 \, \text{D} \]
- For the concave lens:
\[ P_2 = \frac{1}{f_2} = \frac{1}{-0.5} = -2 \, \text{D} \]

### Step 4: Calculate the net power of the combination
- The net power (P_net) of the combination of lenses is the sum of their individual powers:
\[ P_{\text{net}} = P_1 + P_2 = 1.25 - 2 = -0.75 \, \text{D} \]

### Final Answer
- The resulting power of the combined lenses is:
\[ P_{\text{net}} = -0.75 \, \text{D} \]

---