Question

Choose the correct synonym for “Benevolent”.

• A. Cruel
• B. Kind/Generous
• C. Angry
• D. Selfish

Hint:

The word benevolent comes from Latin roots: “bene” (good) and “volent” (wishing). Hence it describes a person who wishes good for others.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given the object distance and focal length for a concave mirror and must find the image distance \( v \) and determine if the image is real or virtual.
Step 2: Key Formula or Approach:
1. Mirror Formula: \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \)
2. Magnification: \( m = -\frac{v}{u} \)
3. Sign Convention: For a concave mirror, \( f \) is negative. Object distance \( u \) is always negative.
Step 3: Detailed Explanation:
Given:
\( u = -15 \) cm
\( f = -10 \) cm
Applying the mirror formula:
\[ \frac{1}{-10} = \frac{1}{v} + \frac{1}{-15} \]
\[ \frac{1}{v} = \frac{1}{15} - \frac{1}{10} \]
Taking LCM of 15 and 10, which is 30:
\[ \frac{1}{v} = \frac{2 - 3}{30} \]
\[ \frac{1}{v} = -\frac{1}{30} \]
\[ v = -30 \text{ cm} \]
Since \( v \) is negative, the image is formed 30 cm in front of the mirror.
A negative \( v \) for a real object in mirrors signifies a real and inverted image.
Step 4: Final Answer:
The image is formed 30 cm in front of the mirror and is real and inverted.