A magnifying glass is to be used at the fixed object distance of 1 inch. If it is to produce an erect image magnified 5 times its focal length should be

Options

A. `0.2` inch
B. `0.8` inch
C. `1.25` inch
D. `5` inch

Explanation

To solve the problem of determining the focal length of a magnifying glass (convex lens) used at a fixed object distance of 1 inch to produce an erect image magnified 5 times, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Object distance (U) = -1 inch (negative because the object is on the same side as the incoming light).
- Magnification (M) = +5 (positive because the image is erect).

2. **Write the Magnification Formula:**
The magnification (M) for a lens is given by the formula:
\[ M = \frac{F}{F + U} \]
where F is the focal length of the lens.

3. **Substitute the Known Values:**
Plugging in the values we have:
\[ 5 = \frac{F}{F - 1} \]

4. **Cross-Multiply to Solve for F:**
Rearranging the equation gives:
\[ 5(F - 1) = F \]
Expanding this:
\[ 5F - 5 = F \]

5. **Rearranging the Equation:**
Bringing all terms involving F to one side:
\[ 5F - F = 5 \]
Simplifying gives:
\[ 4F = 5 \]

6. **Solve for F:**
Dividing both sides by 4:
\[ F = \frac{5}{4} = 1.25 \text{ inches} \]

7. **Conclusion:**
The focal length of the magnifying glass should be 1.25 inches.

### Final Answer:
The focal length of the magnifying glass should be **1.25 inches**.