An object is placed at a distance 24 cm in front of a convex lens of focal length 8 cm.
Calculate the distance of the image from the lens.
Topic: Lenses and image formation
Answer
Given: convex lens, object distance u = −24 cm, focal length f = +8 cm
(Using the New Cartesian sign convention: distances measured against the incident light are negative, so u is negative; f is positive for a convex lens.)
Lens formula: 1/v − 1/u = 1/f
1/v − 1/(−24) = 1/8 1/v + 1/24 = 1/8 1/v = 1/8 − 1/24 1/v = 3/24 − 1/24 1/v = 2/24 = 1/12 v = +12 cm
The image is 12 cm from the lens, on the opposite side to the object (v is positive, so the image is real).
Substitute the SIGNS, not just the numbers. The object is always on the incoming side, so u is always negative for a real object — that is what turns the −1/u in the formula into +1/24. Putting u in as +24 gives 1/v = 1/8 + 1/24 and a wrong answer of 6 cm.
Take the common denominator carefully: 1/8 is 3/24, so 1/8 − 1/24 = 2/24 = 1/12. And remember to invert at the end — you have found 1/v, not v. Writing v = 1/12 cm instead of 12 cm is a surprisingly common slip.
The positive v tells you the image is real and on the far side, which fits: the object at 24 cm is beyond 2F (2 × 8 = 16 cm), so the image should be real, inverted and diminished, between F and 2F. 12 cm is indeed between 8 and 16.