Question

A converging lens produces a four times magnified and upright image of an object placed in front of it. If the focal length of the lens is 11cm. Calculate the object distance.

Please show step to step working and explain as if you are explaining to a child.

Answer 1

We use two standard lens formulas:
- Magnification m = −v/u (v = image distance, u = object distance; signs follow the usual convention).
- Lens equation 1/f = 1/u + 1/v (f = focal length).

Step 1 — use the magnification:
You are told the image is upright and 4× magnified, so m = +4. From m = −v/u:
−v/u = 4 ⇒ v = −4u.
(An upright image for a single lens means the image is virtual and on the same side as the object, so v is negative.)

Step 2 — put v into the lens equation:
1/f = 1/u + 1/v = 1/u + 1/(−4u) = 1/u − 1/(4u) = (3/4)(1/u).

So 1/f = 3/(4u) ⇒ u = 3f/4.

Step 3 — plug in f = 11 cm:
u = 3 × 11 cm / 4 = 33/4 cm = 8.25 cm.

So the object is 8.25 cm in front of the lens. (The image distance would be v = −4u = −33 cm, i.e. a virtual image 33 cm on the same side as the object.)