A complete Class 10 Physics guide to lenses and mirrors — types, ray diagrams, sign convention, lens formula, lens maker's formula, magnification, mirror formula, uses, and four fully solved numerical problems.
Last updated: September 21, 2026
A lens is a piece of transparent material (usually glass) bound by two surfaces, at least one of which is curved, that refracts light to form an image. Lenses are broadly classified into convex lenses and concave lenses based on their shape and the way they bend light.
A convex lens is thicker at the centre and thinner at the edges. It is also called a converging lens because it converges (brings together) a parallel beam of light to a single point called the principal focus. Convex lenses can form both real and virtual images depending on the position of the object.
A concave lens is thinner at the centre and thicker at the edges — the opposite shape of a convex lens. It is also called a diverging lens because it spreads out (diverges) a parallel beam of light, making the rays appear to originate from a point on the same side as the incident light. A concave lens always forms a virtual, erect, and diminished image, regardless of the object's position.
Figure 1: A convex lens converges parallel rays to a real focal point (F). A concave lens diverges parallel rays; the refracted rays appear to come from a virtual focal point on the incident side (dashed lines).
Lenses are classified by the curvature of their two surfaces:
A convex lens is always a converging lens in air, because it is thicker at the centre and bends parallel rays inward toward a real focal point. A concave lens is always a diverging lens in air, spreading rays outward from an apparent (virtual) focal point.
To construct a ray diagram for a convex lens, we use any two of these three principal rays from a point on the object:
Figure 2: When the object is placed beyond 2F, the convex lens forms a real, inverted, and diminished image between F and 2F on the other side.
| Object Position | Image Position | Nature of Image |
|---|---|---|
| At infinity | At focus (F) | Real, inverted, highly diminished |
| Beyond 2F | Between F and 2F | Real, inverted, diminished |
| At 2F | At 2F (other side) | Real, inverted, same size |
| Between F and 2F | Beyond 2F | Real, inverted, magnified |
| At focus (F) | At infinity | Real, inverted, highly magnified |
| Between F and optical centre | Same side as object | Virtual, erect, magnified |
A concave lens always produces a virtual, erect, and diminished image located between the optical centre and the focus, on the same side as the object — regardless of how far the object is placed.
Figure 3: A concave lens always forms a virtual, erect, and diminished image between the optical centre and the focus, on the same side as the object.
To use lens and mirror formulas consistently, physicists follow the New Cartesian Sign Convention:
Figure 4: The Cartesian sign convention — distances to the right of the optical centre (direction of incident light) are positive; distances to the left are negative.
Convex Lens: f = +ve | Concave Lens: f = −ve
The focal length of a convex lens is always positive because it converges light to a real focus located on the side opposite to the incoming light (positive direction). The focal length of a concave lens is always negative because its focus is virtual, located on the same side as the incident light (negative direction).
| Quantity | Convex Lens | Concave Lens |
|---|---|---|
| Focal length (f) | Positive (+) | Negative (−) |
| Object distance (u) | Always negative | Always negative |
| Image distance (v) — real image | Positive | Not possible |
| Image distance (v) — virtual image | Negative | Always negative |
| Power (P = 1/f) | Positive (converging) | Negative (diverging) |
1/v − 1/u = 1/f
Where v = image distance from optical centre, u = object distance from optical centre, and f = focal length of the lens. This single formula, combined with the sign convention, works for both convex and concave lenses and for both real and virtual images.
1/f = (n − 1) × (1/R₁ − 1/R₂)
The lens maker's formula relates the focal length of a lens to the properties of the lens material and the geometry of its surfaces. Here:
This formula is essential when a lens is manufactured — it allows opticians and lens makers to determine the required curvature of the glass surfaces to achieve a desired focal length.
When two thin lenses of focal lengths f₁ and f₂ are placed in contact, the combined focal length F is given by: 1/F = 1/f₁ + 1/f₂, and the combined power is P = P₁ + P₂.
m = h'/h = v/u
Where h' = height of the image, h = height of the object, v = image distance, and u = object distance.
Just as lenses are classified as convex/concave, spherical mirrors are classified as concave mirrors (converging, reflecting surface curves inward like the inside of a spoon) and convex mirrors (diverging, reflecting surface curves outward).
1/v + 1/u = 1/f
Note the + sign (unlike the lens formula's − sign) because for mirrors, both the object and its reflected image lie on the same side.
| Quantity | Concave Mirror | Convex Mirror |
|---|---|---|
| Focal length (f) | Negative (−) | Positive (+) |
| Radius of curvature (R) | Negative (−) | Positive (+) |
| Nature of image | Real or virtual (depends on object position) | Always virtual, erect, diminished |
A concave mirror converges reflected light and is used in torches, headlights, shaving/makeup mirrors, solar cookers, and reflecting telescopes. A convex mirror always forms a virtual, erect, diminished image with a wider field of view, making it ideal for vehicle rear-view mirrors and security mirrors in shops.
Refraction is the bending of light as it passes from one transparent medium to another due to a change in its speed. This is the fundamental phenomenon behind how lenses form images — light bends at each curved surface of the lens according to Snell's Law: n₁ sinθ₁ = n₂ sinθ₂.
When light travels from a rarer medium (like air) to a denser medium (like glass), it bends toward the normal. When it exits back into air, it bends away from the normal. This double refraction at the two curved surfaces of a lens is what causes convex lenses to converge and concave lenses to diverge light.
Diffraction is the bending and spreading of light waves as they pass around obstacles or through narrow openings (apertures) comparable in size to the wavelength of light. Unlike refraction (which occurs due to a change of medium), diffraction is a wave phenomenon that occurs even in a single uniform medium.
Diffraction is commonly demonstrated and measured using a diffraction grating — a plate with a large number of closely spaced parallel slits, used to split and diffract light into several beams travelling in different directions, allowing precise measurement of the wavelength of light.
Myopia (near-sightedness or short-sightedness) is a common eye defect in which a person can see nearby objects clearly but distant objects appear blurred. This happens because the image of a distant object forms in front of the retina instead of exactly on it, usually due to elongation of the eyeball or excessive curvature of the cornea/lens.
Myopia is corrected using a concave (diverging) lens of an appropriate negative focal length. The concave lens diverges the incoming parallel rays slightly before they enter the eye, so that the eye's own lens can now focus the image exactly on the retina.
P = 1/f (f in metres, P in dioptres D)
The power of a lens is a measure of its ability to converge or diverge light rays. It is defined as the reciprocal of the focal length (in metres). The SI unit of power is the dioptre (D). A convex lens has positive power (converging), and a concave lens has negative power (diverging). The optical power prescribed by an eye doctor for spectacles (e.g., −2.5 D for myopia) refers to this quantity.
Question: An object 5 cm in length is held 25 cm away from a converging (convex) lens of focal length 10 cm. Draw the ray diagram and find the position, size, and nature of the image formed.
Solution:
Given: h = +5 cm, u = −25 cm, f = +10 cm (convex lens)
Using the lens formula: 1/v − 1/u = 1/f
1/v = 1/f + 1/u = 1/10 + (−1/25) = 1/10 − 1/25
1/v = (5 − 2)/50 = 3/50
v = 50/3 = +16.67 cm
Magnification: m = v/u = 16.67/(−25) = −0.67
Image height: h' = m × h = −0.67 × 5 = −3.33 cm
Result: The image is formed at 16.67 cm on the other side of the lens. Since v is positive and m is negative, the image is real, inverted, and diminished (height 3.33 cm), located between F (10 cm) and 2F (20 cm) — consistent with the object being placed beyond 2F (25 cm > 20 cm).
Question: A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal in size to the object? Also find the power of the lens.
Solution:
Since the image is real, inverted, and equal in size to the object, the object must be placed at 2F, and the image also forms at 2F on the other side.
Given: v = +50 cm (image distance, real image)
Since |m| = 1 for equal-size image, and the image is real (inverted): m = v/u = −1, so u = −v = −50 cm
The needle is placed at u = −50 cm, i.e., 50 cm in front of the lens (which is the 2F point).
Using the lens formula: 1/v − 1/u = 1/f
1/f = 1/50 − 1/(−50) = 1/50 + 1/50 = 2/50 = 1/25
f = +25 cm = +0.25 m
Power: P = 1/f = 1/0.25 = +4 D
Result: The needle is placed 50 cm in front of the lens, and the power of the lens is +4 dioptres.
Question: Find the power of a concave lens of focal length 2 m.
Solution:
Given: f = −2 m (concave lens — focal length is always negative)
Power: P = 1/f = 1/(−2) = −0.5 D
Result: The power of the concave lens is −0.5 dioptres. The negative sign confirms it is a diverging lens.
Question: A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.
Solution:
Given: f = −15 cm (concave lens), v = −10 cm (concave lens always forms a virtual image on the same side, so v is negative)
Using the lens formula: 1/v − 1/u = 1/f
1/u = 1/v − 1/f = 1/(−10) − 1/(−15)
1/u = −1/10 + 1/15 = (−3 + 2)/30 = −1/30
u = −30 cm
Result: The object is placed 30 cm in front of the concave lens. Since |v| = 10 cm < |u| = 30 cm, the image is diminished, virtual, and erect — as expected for any concave lens, and lies between the optical centre and the focus (15 cm), consistent with v = 10 cm.
| Property | Convex Lens | Concave Lens |
|---|---|---|
| Shape | Thick at centre, thin at edges | Thin at centre, thick at edges |
| Also called | Converging lens | Diverging lens |
| Effect on parallel rays | Converges to a point | Diverges (spreads out) |
| Focal length sign | Positive (+) | Negative (−) |
| Power sign | Positive (+) | Negative (−) |
| Image formed | Real or virtual (depends on object position) | Always virtual, erect, diminished |
| Common use | Magnifying glass, hypermetropia correction | Myopia correction |
| Lens Formula | 1/v − 1/u = 1/f |
| Lens Maker's Formula | 1/f = (n−1)(1/R₁ − 1/R₂) |
| Magnification | m = h'/h = v/u |
| Mirror Formula | 1/v + 1/u = 1/f |
| Power of Lens | P = 1/f (dioptres, f in metres) |
Practice these concepts with hands-on lab experiments that are part of standard worldwide physics curricula. Click any experiment to try the demo.
Determine the focal length of a convex lens using the u-v method on an optical bench, and verify the lens formula experimentally.
Try DemoFind the focal length of a concave mirror using the u-v method and verify the mirror formula 1/v + 1/u = 1/f.
Try DemoDetermine the refractive index of a glass prism by measuring the angle of minimum deviation using a spectrometer — a direct application of refraction.
Try DemoDetermine the wavelength of laser light by measuring diffraction angles using a diffraction grating — demonstrating the wave nature of light.
Try DemoA convex lens is thicker at the centre and converges parallel light rays to a real focal point (converging lens, +f). A concave lens is thinner at the centre and diverges parallel light rays, with a virtual focal point (diverging lens, −f). A convex lens can form real or virtual images depending on object position; a concave lens always forms a virtual, erect, diminished image.
Using the New Cartesian Sign Convention: all distances are measured from the optical centre; distances in the direction of incident light are positive, and against it are negative; heights above the axis are positive, below are negative. The object distance (u) is always negative. A convex lens has f = +ve, and a concave lens has f = −ve.
The focal length of a convex lens is always positive (+f) because it forms a real focus on the side opposite to the incoming light, which is the positive direction as per the sign convention.
The focal length of a concave lens is always negative (−f) because its focal point is virtual and lies on the same side as the incident light, which is the negative direction.
The lens maker's formula is 1/f = (n − 1)(1/R₁ − 1/R₂), relating the focal length to the refractive index (n) of the lens material and the radii of curvature (R₁, R₂) of its two surfaces. It is used to design lenses with a specific required focal length.
Convex lenses are used in magnifying glasses, microscopes, cameras, telescopes, projectors, and to correct hypermetropia. Concave lenses are used to correct myopia, in Galilean telescope eyepieces, laser beam expanders, and peepholes/door viewers.
Myopia (short-sightedness) is a defect where distant objects appear blurred because their image forms in front of the retina instead of on it. It is corrected by wearing eyeglasses with a concave (diverging) lens of appropriate negative power, which diverges incoming rays before they reach the eye so the image falls exactly on the retina.
The mirror formula is 1/v + 1/u = 1/f, applicable to both concave and convex mirrors. As per sign convention: a concave mirror has a negative focal length (real focus in front of the mirror), while a convex mirror has a positive focal length (virtual focus behind the mirror).
Refraction is the bending of light when it passes from one transparent medium to another due to a change in speed (e.g., light bending as it enters a lens). Diffraction is the bending/spreading of light waves around obstacles or through narrow slits, occurring even within a single medium, and is best observed using a diffraction grating.
Magnification is given by m = h'/h = v/u, where h' is image height, h is object height, v is image distance, and u is object distance. A negative m means a real, inverted image; a positive m means a virtual, erect image.
