Statement-1: In a simple microscope, angular height of image is same as angular height of object Statement-2 : Least distance of distinct vision for an eye is `25 cm`. If object is placed at a distance less than 25 cm angular height increases.

Options

A. Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of statement 1.
B. Statement 1 is false, Statement 2 is true
C. Statement 1 is true, Statement 2 is false
D. statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of statement 1.

Answer

To solve the problem, we need to analyze both statements provided in the question and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** In a simple microscope, the angular height of the image is the same as the angular height of the object.

- A simple microscope uses a convex lens to magnify an object. When an object is placed between the focal point (F) and the optical center (O) of the lens, the rays of light diverge after passing through the lens.
- The angular height of the object is defined as the angle subtended by the object at the eye. Similarly, the angular height of the image is defined as the angle subtended by the image at the eye.
- By constructing a diagram, we can see that the angles formed by the rays from the object and the image are the same. Therefore, the angular height of the image is indeed the same as the angular height of the object.

**Conclusion for Statement 1:** True.

### Step 2: Analyze Statement 2
**Statement 2:** The least distance of distinct vision for an eye is 25 cm. If the object is placed at a distance less than 25 cm, angular height increases.

- The least distance of distinct vision (D) for a normal human eye is approximately 25 cm. This means that objects closer than this distance can appear blurred.
- As the object is moved closer to the eye (less than 25 cm), the angle subtended by the object at the eye increases. This is due to the geometry of the situation; as the distance decreases, the angle increases.
- Therefore, if the object is placed at a distance less than 25 cm, the angular height indeed increases.

**Conclusion for Statement 2:** True.

### Step 3: Determine the Relationship Between the Statements
- While both statements are true, Statement 2 does not provide a direct explanation for Statement 1. Statement 1 discusses the angular height of the image and object in the context of a simple microscope, while Statement 2 discusses the effect of distance on angular height in general.
- Therefore, while both statements are true, Statement 2 does not explain Statement 1.

### Final Conclusion
- Both statements are true, but Statement 2 is not the correct explanation of Statement 1. Thus, the correct answer is option 4.