Ray optics (Class 12): mirrors, lenses, prisms and instruments in 3D
Ray optics treats light as straight rays that bend at surfaces. With a few formulas you can place the image made by a mirror or a lens, find the critical angle, and predict what a microscope or a telescope shows. These labs let you move the object and watch the rays.
NCERT Class 12 Physics, Chapter 9 (Ray Optics and Optical Instruments). Every lab below runs in 3D in your browser or on a phone, in English and Hindi.
Try the labs
Refraction, Snell's law, critical angle and total internal reflection · plan · Chapter 9
To verify Snell's law of refraction, find refractive index, critical angle, and observe total internal reflection.
Convex and concave lenses, lens maker's formula · plan · Chapter 9
To study image formation by convex and concave lenses for different object positions and to verify the lens formula and magnification.
Concave and convex mirrors: image formation · free · Chapter 9
To study image formation by concave and convex mirrors and verify the mirror formula and magnification.
Prism: deviation curve and dispersion · plan · Chapter 9
To trace light through a prism, find the angle of minimum deviation and the refractive index, and understand dispersion.
Refractive index of a glass slab with a travelling microscope · plan · Chapter 9
To determine the refractive index of a glass slab using a travelling microscope.
Focal length of a concave lens (lens-combination method) · plan · Chapter 9
To find the focal length of a concave lens by combining it (in contact) with a convex lens of smaller focal length.
Human eye and its defects (myopia, hypermetropia) · plan · Chapter 9
To understand image formation in the human eye, accommodation, and the correction of myopia, hypermetropia and presbyopia with spectacles.
Compound microscope and telescopes · plan · Chapter 9
To study the compound microscope and telescopes: ray diagrams, magnifying power and the length of the instrument.
Optical fibre: acceptance angle, numerical aperture and dispersion · plan · Chapter 9
To study how light is guided in an optical fibre by total internal reflection, and to find the acceptance angle, numerical aperture and modal dispersion.
Rainbow: refraction and internal reflection in a water drop · plan · Chapter 9
To understand the formation of the primary and secondary rainbows by refraction, internal reflection and dispersion in water drops.
Two-lens system: image, magnification and equivalent focal length · plan · Chapter 9
To find the final image formed by two thin lenses separated by a distance d, its magnification and the equivalent focal length of the combination.
Reflection and refraction
A ray reflects with angle of incidence equal to the angle of reflection. On entering a denser medium it bends towards the normal, following Snell's law n₁ sin i = n₂ sin r.
When light goes from a denser to a rarer medium and the angle of incidence exceeds the critical angle, sin C = n₂/n₁, it is totally reflected. This is how optical fibres and diamonds work.
n₁ sin i = n₂ sin rsin C = 1/napparent depth = real depth / n
Mirrors and lenses
Both use the Cartesian sign convention, with distances measured from the pole or optical centre and the incident light travelling to the right. A real image has a positive v for a lens and a negative v for a mirror.
The lens maker's formula links focal length to the refractive index and the two radii of curvature.
1/v − 1/u = 1/f (lens)1/v + 1/u = 1/f (mirror)m = v/u (lens), m = −v/u (mirror)1/f = (n − 1)(1/R₁ − 1/R₂)P = 1/f (in metres), unit dioptre
Prism and instruments
A prism deviates light by the least amount when the ray passes symmetrically; then n = sin((A + δm)/2) / sin(A/2). Different colours bend by different amounts, which is dispersion and also the cause of a rainbow.
A compound microscope gives a large magnification with a short-focus objective and eyepiece. An astronomical telescope in normal adjustment has magnifying power fo/fe.
n = sin((A + δm)/2) / sin(A/2)M (telescope) = fo / feM (microscope) ≈ (L/fo)(D/fe)
Frequently asked questions
What is the sign convention for lenses and mirrors?
Take the pole or optical centre as origin, the direction of incident light as positive. Distances against the light are negative, so the object distance u is always negative for a real object.
Why does a diamond sparkle?
Its refractive index is about 2.4, so the critical angle is only about 24°. Most rays inside suffer total internal reflection several times before leaving.
What is the power of a lens?
It is the reciprocal of the focal length in metres. A convex lens of focal length 25 cm has power +4 dioptre.
Why is the sky blue and the sunset red?
Air scatters short wavelengths (blue) far more than long ones (red), as Rayleigh scattering varies as 1/λ⁴. At sunset the long path removes the blue and leaves the red.