STATEMENT-`1` We cannot produce a real image by plane or convex mirror under any circumstances.
STATEMENT-`2` The focal length of a convex mirror is always taken as positive.

Options

A. Statement is True, Statement II is True, Statement II is correct explanation for Statement I
B. Statement I is True, Statement II is True, Statement II is NOT a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To analyze the statements provided in the question, we will evaluate each statement separately and determine their truth values.

### Step 1: Evaluate Statement 1
**Statement 1:** "We cannot produce a real image by plane or convex mirror under any circumstances."

- **Analysis:** This statement is incorrect. A real image can be produced by a plane or convex mirror if the incident rays are converging. For instance, if parallel rays converge before reaching the mirror, they can reflect off the mirror and form a real image. Thus, it is possible to produce a real image under specific conditions.

**Conclusion for Statement 1:** False

### Step 2: Evaluate Statement 2
**Statement 2:** "The focal length of a convex mirror is always taken as positive."

- **Analysis:** This statement is true. In optics, the focal length of a convex mirror is defined as positive because, by convention, distances measured in the direction of the incoming light rays are considered positive. Since the focus of a convex mirror lies behind the mirror (in the direction from which the light comes), it is assigned a positive value.

**Conclusion for Statement 2:** True

### Step 3: Determine the Relationship Between the Statements
- Statement 1 is false, and Statement 2 is true. There is no direct relationship between the two statements; they address different aspects of mirror optics.

### Final Conclusion
- **Statement 1:** False
- **Statement 2:** True

Based on the evaluations, the correct option is that Statement 1 is false and Statement 2 is true.

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