Question

Define the principal axis of a concave mirror.

Answer 1

Step 1: Understand the structure of a concave mirror:
A concave mirror is a spherical mirror with an inward curve, resembling the interior of a sphere.

Step 2: Key parts of a concave mirror:
- Pole (P): The central point of the mirror's surface.
- Center of Curvature (C): The center of the imaginary sphere from which the mirror is a segment.

Step 3: Define the principal axis:
- The principal axis is a straight line connecting the pole (P) and the center of curvature (C) of the mirror.
- This axis serves as a reference for analyzing light ray reflections.

Step 4: Conclusion:
The principal axis of a concave mirror is the straight line that extends through its pole and center of curvature.

Answer 2

Step 1: Understand the behavior of light in a concave mirror:
- A ray of light incident parallel to the principal axis of a concave mirror reflects through the focus (F).

Step 2: Interpret the given information:
- The reflected ray passes through a point on the principal axis 10 cm from the pole (P).
- Thus, the focal length (f) of the concave mirror is 10 cm.

Step 3: Use the relationship between focal length and radius of curvature:
For spherical mirrors, the relation is:
\[R = 2f\]

Step 4: Substitute the known value:
\[R = 2 \times 10\,\text{cm} = 20\,\text{cm}\]

Step 5: Conclusion:
The radius of curvature of the concave mirror is 20 cm.

Answer 3

Step 1: Identify mirror type and sign conventions:
- The mirror is convex.
- For convex mirrors:
   - Focal length (f) is positive.
    - Object distance (u) is negative (object in front).

Step 2: Record given values:
Object distance, u = -10 cm
Focal length, f = +15 cm

Step 3: Apply the mirror formula:
\[\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\]
Substitute values:
\[\frac{1}{15} = \frac{1}{v} + \frac{1}{-10}\]

Step 4: Solve the equation for 1/v:
\[\frac{1}{v} = \frac{1}{15} + \frac{1}{10}= \frac{2}{30} + \frac{3}{30}= \frac{5}{30}= \frac{1}{6}\]

Step 5: Calculate image distance (v):
\[v = 6 \text{ cm}\]

Step 6: Interpret the result:
A positive \( v \) indicates the image is formed behind the convex mirror.
The image is virtual, erect, and diminished.

Final Answer:
The image is located 6 cm behind the mirror.

Answer 4

A convex mirror produces a virtual, erect, and diminished image.
Ray Diagram:

Explanation:
1. Ray 1 (Red): Incident parallel to the principal axis reflects as if originating from the focus (F).
2. Ray 2 (Green): Incident towards the center of curvature (C) reflects back along its original path.
The image (I) is formed by the apparent intersection of reflected rays behind the mirror. This image is virtual, erect, and diminished.