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 combined convex lens and 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 (positive because it is a convex lens).
- The focal length of the concave lens (F2) is given as -50 cm (negative because it is a concave lens).

### Step 2: Use the formula for combined focal length
The formula for the combined focal length (F_eq) of two lenses in combination is:
\[ \frac{1}{F_{eq}} = \frac{1}{F_1} + \frac{1}{F_2} \]

### Step 3: Substitute the values into the formula
Substituting the values of F1 and F2 into the formula:
\[ \frac{1}{F_{eq}} = \frac{1}{80} + \frac{1}{-50} \]

### Step 4: Find a common denominator and calculate
The common denominator for 80 and 50 is 400. Therefore, we rewrite the fractions:
\[ \frac{1}{F_{eq}} = \frac{5}{400} - \frac{8}{400} = \frac{5 - 8}{400} = \frac{-3}{400} \]

### Step 5: Calculate the equivalent focal length
Now, we can find F_eq:
\[ F_{eq} = \frac{400}{-3} \text{ cm} = -\frac{400}{3} \text{ cm} \]

### Step 6: Convert focal length to meters
To convert the focal length from centimeters to meters:
\[ F_{eq} = -\frac{400}{3} \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = -\frac{4}{3} \text{ m} \]

### Step 7: Calculate the power of the combined lens
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{F_{eq}} \text{ (in meters)} \]
Substituting the value of F_eq:
\[ P = \frac{1}{-\frac{4}{3}} = -\frac{3}{4} \text{ diopters} = -0.75 \text{ diopters} \]

### Final Answer
The resulting power of the combined lenses is **-0.75 diopters**.

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