An object is approaching a convex lens of focal length 0.3m with a speed of `0.01m s^(-1)`. Find the magnitudes of the ratio of change of position and lateral magnification of image when the object is at a distance of 0.4m from the lens

Explanation

To solve the problem, we need to find the magnitudes of the ratio of change of position and lateral magnification of the image when the object is at a distance of 0.4 m from the lens. Let's break this down step by step.

### Step 1: Identify Given Values
We are given:
- Focal length of the lens, \( f = 0.3 \, \text{m} \)
- Object distance, \( u = -0.4 \, \text{m} \) (the negative sign indicates that the object is on the same side as the incoming light)
- Speed of the object, \( \frac{du}{dt} = -0.01 \, \text{m/s} \) (negative because the object is approaching the lens)

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