NCERT Class 10 Science — Chapter 9, Light: Reflection and Refraction
How do you use the lens formula to find the image distance?
The lens formula is 1/v − 1/u = 1/f, where u is the object distance, v the image distance and f the focal length. Rearrange it to 1/v = 1/f + 1/u, substitute with signs from the Cartesian convention, then take the reciprocal. The sign of v tells you whether the image is real or virtual.
The sign convention is where most marks are lost
Almost every wrong answer in this topic comes from signs, not arithmetic. Distances are measured from the optical centre, with the incoming light travelling left to right. Anything measured against that direction is negative, which means a real object placed in front of the lens always has a NEGATIVE u.
A converging (convex) lens has a positive f; a diverging (concave) lens has a negative f. Get those two right and the formula does the rest — but write u as a positive number and every subsequent step will be confidently, invisibly wrong.
Reading the answer once you have v
A positive v means the image forms on the far side of the lens and is real and inverted. A negative v means the light only appears to come from that point, so the image is virtual and upright, and it sits on the same side as the object.
Magnification is m = v/u. If |m| is greater than 1 the image is enlarged, less than 1 diminished. A negative m means inverted — which for a lens always accompanies a real image, so the two readings should agree. If they do not, you have a sign error upstream.
Why the exam rewards the method, not the number
CBSE marking schemes award marks for the formula, the substitution and the result separately. A student who writes the formula and substitutes correctly but slips in the final division still scores most of the marks; a student who writes only a correct final number scores fewer.
That is worth internalising, because it is also how you should practise: get the method reliable first, and treat the arithmetic as the easy part it actually is.
A worked example
An object is placed 30 cm in front of a convex lens of focal length 10 cm. Find the image distance and describe the image.
- Write the formula1/v − 1/u = 1/ff = 10 cm, u = -30 cm
- Substitute and solve for v1/v = 1/f + 1/uv = 15 cm
- Magnificationm = v/um = -0.5
- Read the imagesign of v → real/virtual, sign of m → orientationreal, inverted, diminished
⚙️ Every number above was computed by Bolo’s Lens Lab engine when this page was built — the same code that checks your answer inside the app, not a hand-typed solution.
Now try it yourself
Reading a solution is the easy half. In the Lens Lab you set the values and the engine checks each step — and if you get stuck it shows you the method before it shows the answer.
Open the Lens Lab →Common questions
Why is the object distance negative in the lens formula?
Because distances are measured from the optical centre against the direction the light travels. Light goes left to right, a real object sits to the left, so its distance is negative under the Cartesian sign convention. Writing it as positive is the single most common source of wrong answers in this chapter.
What does a negative image distance mean?
That the image is virtual. The rays never actually meet; they only appear to diverge from that point, so the image sits on the same side as the object and is upright. You cannot catch a virtual image on a screen, which is the practical test examiners expect you to know.
Is the lens formula the same for concave lenses?
Yes, the formula is identical. The only difference is that a concave lens has a negative focal length, and that sign carries through the arithmetic on its own. This is why the convention matters more than memorising separate cases — one formula covers both lenses.