Ray Optics and Optical InstrumentsNEET Physics · Class 12 · NCERT Chapter 9

Introduction

Ray optics treats light as straight lines that obey two laws: reflection (angle of incidence = angle of reflection) and refraction (Snell's law). It is an excellent approximation when the size of objects, mirrors and lenses is much larger than the wavelength of light. Almost everything you see in everyday life, your reflection in a mirror, a lens in your spectacles, a telescope, the rainbow, comes from these two laws.

Expect 2 to 3 NEET questions every year. Common asks: image formation by spherical mirrors and thin lenses, lens-maker formula, total internal reflection, prism (deviation, dispersion), and microscope or telescope magnification.

Cartesian sign convention

Pick the pole P (or optical centre O) as origin. The incident light travels in the positive x direction. Rules:

• All distances measured from P (or O), along the principal axis.
• Distances in the direction of incident light: positive. Against it: negative.
• Heights above the principal axis: positive. Below: negative.

Consequence: real objects have u < 0. Real images formed in front of a mirror have v < 0. For a convex lens, real image on the other side has v > 0. Concave mirror f < 0; convex mirror f > 0. Convex lens f > 0; concave lens f < 0.

Spherical mirrors

A spherical mirror is part of a hollow sphere. Concave (caved in, reflecting on the inner side) is converging. Convex (bulged out) is diverging. The relevant points are the pole P, centre of curvature C and principal focus F. For a paraxial ray (close to axis):

Drag the object distance to see the image position move along the principal axis. Image direction reflects Cartesian convention.

Mirror formula and magnification

Sign of m tells you erect or inverted (positive m: erect; negative m: inverted). |m| tells you size (greater than 1: magnified; less than 1: diminished).

Cartesian sign convention: distances measured from the pole; against the incident light (left side) are negative. Concave mirror: f < 0. Convex mirror: f > 0.

Refraction and Snell's law

At the interface between two media of refractive indices n_1 and n_2:

Going rarer to denser (n_1 < n_2): light bends towards the normal. Going denser to rarer (n_1 > n_2): light bends away from the normal. Refractive index n = c / v, where v is the speed of light in the medium.

Drag the angle slider and watch how the refracted ray bends. Snell's law: n_1 sin θ_1 = n_2 sin θ_2.

Apparent depth

Looking down on an object submerged in a medium, the apparent depth is less than the real depth:

Apparent shift: $\Delta =d(1-1/n)$. A coin at 8 cm in water (n = 1.33) looks at about 6 cm; a glass slab of thickness t shifts an object behind it forward by t (1 - 1/n).

Looking from above, the water bends light from the fish so it appears closer to the surface than it really is.

Total internal reflection

When light goes from denser to rarer (e.g. glass to air), the refracted ray bends away from the normal. As θ_1 increases, θ_2 reaches 90° at a special angle called the critical angle θ_c:

For θ_1 > θ_c, no refraction is possible: all light reflects back internally. Applications: optical fibres (signal trapped in core by repeated TIR), prismatic binoculars (two TIR replace two mirrors), brilliance of diamonds (n = 2.42, θ_c = 24.4°).

Going denser → rarer (e.g. glass → air), angles above the critical angle give total internal reflection.

Refraction at a spherical surface

For a single refracting spherical surface of radius R between media n_1 and n_2:

Used to derive the lens-maker formula by treating a thin lens as two such surfaces.

Lens-maker formula

For a thin lens of refractive index n with surface radii R_1 (first hit) and R_2 (second):

Sign convention for R: positive if convex to incoming light, negative if concave. A symmetric biconvex lens with |R| = R: $f=R/(2(n-1))$. For glass (n = 1.5) and R = 20 cm, f = 20 cm.

Sign convention for radii: R is positive if the surface is convex to the incoming light, negative if concave. Biconvex: R_1 > 0, R_2 < 0.

Thin lens formula and magnification

Convex lens (f > 0): produces a real, inverted image when object is beyond F; virtual, erect, magnified when inside F (magnifier). Concave lens (f < 0): always gives a virtual, erect, diminished image.

Drag the object distance to see how the image moves and changes character. Light travels left to right; u is negative.

Power of a lens and combination

Power P (in diopters) measures bending strength:

Two thin lenses in contact:

Two lenses separated by distance d:

Two thin lenses in contact behave like a single equivalent lens. Powers add. Separated lenses use a slightly different formula.

Prism: deviation and dispersion

For a prism of refracting angle A and refractive index n, with angles of incidence i_1, i_2 and refraction r_1, r_2 inside:

Plot δ against i_1: it has a minimum at the symmetric configuration (i_1 = i_2, r_1 = r_2 = A/2). At minimum deviation:

For thin prisms (A < 10°): $\delta =(n-1)A$.

Dispersion

Different colours have slightly different n, so they deviate differently. The angular spread between violet and red is the angular dispersion:

Dispersive power (a property of the material):

Sliding the angle of incidence finds the minimum deviation: at min deviation, i_1 = i_2 and the ray inside the prism is parallel to the base.

Microscope and telescope

Simple microscope (a single converging lens used as a magnifier):

Compound microscope (objective f_o + eyepiece f_e, tube length L):

Pick small f_o (objective close to specimen) and small f_e for high magnification.

Astronomical (refracting) telescope, normal adjustment (final image at infinity):

Pick a long-focal-length objective and a short-focal-length eyepiece.

D = 25 cm (near point of a normal eye). Switch between simple microscope, compound microscope and astronomical telescope.

Human eye and defects (brief)

• Myopia (short-sight): image forms before retina; corrected by a concave (diverging) lens.
• Hypermetropia (long-sight): image forms beyond retina; corrected by a convex (converging) lens.
• Presbyopia: ageing eye loses focusing range; bifocal lenses help.
• Astigmatism: uneven curvature of cornea; corrected by a cylindrical lens.

Worked NEET problems

Summary cheat sheet

• Mirror formula: $1/v+1/u=1/f$, $m=-v/u$.
• Concave mirror: f < 0 (converging). Convex mirror: f > 0.
• Snell's law: $n_1\sin {\theta }_1=n_2\sin {\theta }_2$.
• Apparent depth: $d_{\text{app}}=d/n$, shift = d(1 - 1/n).
• TIR: $\sin {\theta }_c=1/n$ (denser to rarer).
• Lens-maker: $1/f=(n-1)(1/R_1-1/R_2)$.
• Thin lens: $1/v-1/u=1/f$, $m=v/u$, P = 1/f(m).
• Combination (contact): $P=P_1+P_2$.
• Prism: $\delta =(n-1)A$ (small A); $n=\sin ((A+{\delta }_m)/2)/\sin (A/2)$.
• Compound microscope: $M=(L/f_o)(1+D/f_e)$.
• Telescope: $M=f_o/f_e$, length $f_o+f_e$.

Next: try the interactive widgets for mirrors, lenses, prisms and instruments, or work through the 32 NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.