Question

An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the position and nature of the image.

• A. 30 cm behind mirror, virtual and erect
• B. 30 cm in front of mirror, real and inverted
• C. 15 cm behind mirror, virtual
• D. 20 cm in front of mirror, real

Hint:

For concave mirrors: - If \(v\) is negative → image forms in front of mirror (real). - If \(v\) is positive → image forms behind mirror (virtual).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This problem involves using mirror optics and sign conventions to locate the image formed by a concave mirror.
Step 2: Key Formula or Approach:
Mirror Formula: \[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]
Sign Convention:
- Object distance (\( u \)) is always negative (\( -15 \) cm).
- Focal length (\( f \)) of a concave mirror is negative (\( -10 \) cm).
Step 3: Detailed Explanation:
Given: \( u = -15 \) cm, \( f = -10 \) cm.
Substituting into the mirror formula:
\[ \frac{1}{v} + \frac{1}{-15} = \frac{1}{-10} \]
\[ \frac{1}{v} = -\frac{1}{10} + \frac{1}{15} \]
Finding the common denominator (30):
\[ \frac{1}{v} = \frac{-3 + 2}{30} \]
\[ \frac{1}{v} = -\frac{1}{30} \]
\[ v = -30 \text{ cm} \]
Since \( v \) is negative, the image is formed on the same side as the object (in front of the mirror).
Images formed in front of the mirror are always real and inverted.
Step 4: Final Answer:
The image is formed 30 cm in front of the mirror and is real and inverted.