Detailed physics worksheet focusing on lens optics, featuring ray tracing exercises and questions about convex and concave lenses.

Let’s solve this step by step.

We’re given a table with object distances (do) and image distances (di) for a convex lens. We need to find the focal length (f) using the lens formula:

1/f = 1/do + 1/di

But wait — look at the data. For Trial 1: do = 30 cm, di = 15 cm
Trial 2: do = 20 cm, di = 20 cm
Trial 3: do = 15 cm, di = 30 cm

These are symmetric! That suggests something special is happening.

In Trial 2, when do = di = 20 cm, that means the object is at 2F, and the image is also at 2F on the other side. In that case, the focal length f should be half of that distance.

So if do = di = 20 cm → then 2f = 20 cm → f = 10 cm

Let’s verify with the lens formula for Trial 1:

1/f = 1/30 + 1/15
= 1/30 + 2/30
= 3/30 = 1/10
→ f = 10 cm ✔

Now Trial 3:

1/f = 1/15 + 1/30
= 2/30 + 1/30
= 3/30 = 1/10
→ f = 10 cm ✔

Perfect! All trials give f = 10 cm.

Also, in the diagram section, they show rays converging after passing through a convex lens — which matches our calculation.

And in the last part, they ask about magnification for Trial 1:

Magnification M = -di/do = -15/30 = -0.5

The negative sign means inverted image, and 0.5 means it’s half the size.

They also ask: “Is the image real or virtual?” Since di is positive (image formed on opposite side of lens from object), it’s a real image.

For Trial 3: M = -di/do = -30/15 = -2 → inverted and twice as big.

All consistent.

Final Answer:
The focal length of the lens is 10 cm.