Convex lens of focal length f is used as simple microscope. D is the least distance for distinct vision.

Options

A. Magnification achieved must be equal to `(D)/(f)`
B. Magnification achieved may be equal to `(D)/(f)`
C. Magnification achieved cannot be less than `1+(D)/(f)`
D. Maximum magnification achieved is equal to `1+(D)/(f)`.

Explanation

To solve the problem regarding the convex lens used as a simple microscope, we need to derive the magnification formula and understand the parameters involved. Here’s a step-by-step solution:

### Step 1: Understand the Setup
A convex lens is used as a simple microscope. The focal length of the lens is denoted as \( f \), and the least distance of distinct vision (the closest distance at which the eye can see an object clearly) is denoted as \( D \).

### Step 2: Define the Magnification
The magnification \( M \) of a simple microscope is defined as the ratio of the size of the image to the size of the object. For a convex lens, the magnification can be expressed as:
\[ M = \frac{v}{u} \]
where \( v \) is the image distance and \( u \) is the object distance.

### Step 3: Lens Formula
We can use the lens formula to relate the object distance \( u \), image distance \( v \), and focal length \( f \):
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Rearranging this gives us:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]

### Step 4: Maximum Magnification
For maximum magnification, the object is placed at the focal point of the lens, and the image is formed at the least distance of distinct vision \( D \). The maximum magnification \( M_{max} \) can be given by:
\[ M_{max} = 1 + \frac{D}{f} \]
This formula indicates that the maximum magnification occurs when the image is at the least distance of distinct vision.

### Step 5: Minimum Magnification
The minimum magnification occurs when the object is placed at the focal point of the lens. In this case, the magnification can be expressed as:
\[ M_{min} = \frac{D}{f} \]

### Step 6: Conclusion
From the above derivations, we conclude that:
- The maximum magnification achievable with a convex lens used as a simple microscope is \( M_{max} = 1 + \frac{D}{f} \).
- The minimum magnification is \( M_{min} = \frac{D}{f} \).