A magnifying glass is a combination of a convex lens of focal length 5 cm and a concave lens of power - 5D. If the distance of distinct vision 20 cm, calculate the magnifying power of the magnifying glass.

Answer

To find the magnifying power of the magnifying glass, we will follow these steps:

### Step 1: Understand the Components
We have a magnifying glass that consists of:
- A convex lens with a focal length \( F_1 = 5 \, \text{cm} \)
- A concave lens with a power \( P_2 = -5 \, \text{D} \)

### Step 2: Convert the Focal Length of the Convex Lens
Convert the focal length of the convex lens from centimeters to meters:
\[ F_1 = 5 \, \text{cm} = 0.05 \, \text{m} \]

### Step 3: Calculate the Focal Length of the Concave Lens
The power \( P \) of a lens is related to its focal length \( F \) by the formula:
\[ P = \frac{1}{F} \]
For the concave lens:
\[ P_2 = -5 \, \text{D} \implies F_2 = \frac{1}{P_2} = \frac{1}{-5} = -0.2 \, \text{m} = -20 \, \text{cm} \]

### Step 4: Calculate the Focal Length of the Combination
Using the formula for the focal length of a combination of lenses in contact:
\[ \frac{1}{F_c} = \frac{1}{F_1} + \frac{1}{F_2} \]
Substituting the values:
\[ \frac{1}{F_c} = \frac{1}{0.05} + \frac{1}{-0.2} \]
Calculating each term:
\[ \frac{1}{0.05} = 20 \quad \text{and} \quad \frac{1}{-0.2} = -5 \]
Thus,
\[ \frac{1}{F_c} = 20 - 5 = 15 \]
So,
\[ F_c = \frac{1}{15} \approx 0.0667 \, \text{m} = 6.67 \, \text{cm} \]

### Step 5: Calculate the Magnifying Power
The formula for the magnifying power \( M \) of a magnifying glass is given by:
\[ M = 1 + \frac{D}{F_c} \]
Where \( D \) is the least distance of distinct vision, given as \( D = 20 \, \text{cm} = 0.2 \, \text{m} \).
Substituting the values:
\[ M = 1 + \frac{0.2}{0.0667} \]
Calculating:
\[ \frac{0.2}{0.0667} \approx 3 \]
So,
\[ M = 1 + 3 = 4 \]

### Final Answer
The magnifying power of the magnifying glass is \( M = 4 \).

---