A particle moves towards a concave mirror of focal length `30cm` along its axis and with a constant speed of `4cm//sec`. At the instant the particle is `90cm` from the pole

Options

A. velocity of image is `1 cm//sec`
B. velocity of image w.r.t. particle is `5cm//sec`
C. particle and image move towards each other
D. as the particle approaches pole, velocity of image increases

Explanation

To solve the problem step by step, we will use the mirror formula and the concept of image velocity in relation to object velocity.

### Step 1: Identify the given values
- Focal length of the concave mirror, \( f = -30 \, \text{cm} \) (negative for concave mirrors)
- Object distance, \( u = -90 \, \text{cm} \) (negative as per sign convention)
- Speed of the object, \( \frac{du}{dt} = -4 \, \text{cm/s} \) (negative because the object is moving towards the mirror)

### Step 2: Use the mirror formula
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