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 teaching a child

Answer 1

Step 1 — Write the formulas
- Thin lens formula: 1/f = 1/v + 1/u
(f = focal length, u = object distance, v = image distance)
- Magnification: m = -v/u
(the minus sign means an inverted image gives negative m; an upright image gives positive m)

Step 2 — Use the given magnification
The image is upright and 4 times bigger, so m = +4. From m = -v/u:
4 = -v/u → v = -4u
(The minus sign on v means the image is virtual and on the same side of the lens as the object.)

Step 3 — Substitute into the lens equation
1/f = 1/v + 1/u = 1/(-4u) + 1/u = -1/(4u) + 1/u = (3/(4u))

So 1/f = 3/(4u) → u = 3f/4

Step 4 — Put f = 11 cm
u = 3 × 11 / 4 = 33/4 = 8.25 cm

So the object is 8.25 cm from the lens.

(Optional) Image distance: v = -4u = -33 cm (the negative sign shows the image is virtual and 33 cm on the same side as the object).