Ray Optics: One Mark Questions, Book Back Answers and Notes

About Ray Optics

Medium ~180 min study

Ray optics, also called geometrical optics, works when the objects and openings light meets are much larger than its wavelength. In that case we can draw light as straight rays and solve problems with geometry. The same idea explains spectacles, camera lenses, optical fibres and the endoscope a doctor uses to see inside the body.

The unit starts with the laws of reflection and moves to refraction, where Snell's law does most of the work. From there you reach total internal reflection, lenses and the prism. Everyday observations fit into this chain: a pencil looks bent in a glass of water because of refraction, and a diamond sparkles because of total internal reflection. The same laws let you calculate the refractive index of a prism or the power of two lenses kept in contact.

Questions from this unit come as both theory and numericals. Practise the Cartesian sign convention until it is automatic, because one wrong sign changes a real image into a virtual one. Learn the derivations of the mirror equation, the lens maker's formula and the prism formula, and be ready to explain why the sky is blue and why the sun looks red at sunset.

What you'll learn

• Use the mirror and lens equations to find the image position and magnification for a given object distance.
• Derive the lens maker's formula from refraction at two spherical surfaces.
• Find the refractive index of a prism from its angle and the angle of minimum deviation.
• State the conditions for total internal reflection and explain how optical fibres use it.
• Explain dispersion and write the expression for dispersive power.
• Explain the blue colour of the sky and the red colour of the sunset using Rayleigh scattering.

Before you start

• Basic geometry of triangles, angles and arcs of circles.
• The idea that light is an electromagnetic wave.
• The fact that light travels fastest in vacuum and slower in materials such as water and glass.

Ray Optics explained

Mirrors, Lenses and Prisms

Reflection and Spherical Mirrors

The laws of reflection apply at every point of a curved mirror. For concave and convex mirrors the mirror equation, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$, gives the image position, and magnification is $m = -\frac{v}{u}$. All distances are measured from the pole using the Cartesian sign convention. Once the signs are right, the answer itself tells you whether the image is real or virtual, erect or inverted. For example, a concave mirror of focal length 10 cm with an object at 15 cm gives $v = -30$ cm: a real, inverted image, twice the size of the object.

Refraction at Plane and Curved Surfaces

Light bends when it passes from one medium to another because its speed changes. Snell's law, $n_1 \sin(i) = n_2 \sin(r)$, connects the two angles. Refraction at a plane surface explains apparent depth, which is why a swimming pool looks shallower than it is, and the lateral shift through a glass slab. When light goes from a denser to a rarer medium and the angle of incidence exceeds the critical angle, $i_c = \sin^{-1}(\frac{1}{n})$ (for the denser medium in air), no light is refracted out. This is total internal reflection, the working principle of optical fibres.

Thin Lenses and Lens Maker's Formula

Using refraction at two curved surfaces, the chapter derives the lens maker's formula, $\frac{1}{f} = (n-1) (\frac{1}{R_1} - \frac{1}{R_2})$. It links focal length to the refractive index of the glass and the radii of curvature of its faces. Power is $P = \frac{1}{f}$ with f in metres, measured in dioptre. For thin lenses in contact the powers simply add, $P = P_1 + P_2$, so a +4 D lens and a -2 D lens together act as a +2 D lens of focal length 50 cm.

Prism Geometry and Dispersion

A ray passing through a prism is refracted at two faces and turns through an angle of deviation. As the angle of incidence increases, the deviation first falls, reaches a minimum value $D_m$, and then rises again. At minimum deviation the ray passes symmetrically through the prism, and the refractive index is $n = \frac{\sin((A+D_m)/2)}{\sin(A/2)}$. Because n is slightly different for each colour, white light spreads into a spectrum. Violet deviates the most and red the least. A rainbow forms the same way, through refraction, dispersion and internal reflection inside raindrops.

Dispersive Power and Scattering

Dispersive power, $\omega$, measures how strongly a material separates colours: $\omega = \frac{n_V - n_R}{n - 1}$, where n is the refractive index for the mean (yellow) colour. It matters when lenses are designed to reduce chromatic aberration. Light is also scattered by particles in the air. In Rayleigh scattering the scattered intensity is proportional to $\frac{1}{\lambda^4}$, so blue light is scattered far more than red. That is why the clear sky is blue at noon, and why the sun and the sky near it look red at sunrise and sunset.

Common mistakes to avoid

• Getting signs wrong. Measure every distance from the pole or optical centre, and take the direction of the incident light as positive.
• Mixing up power and focal length. P = 1/f only when f is in metres, so 20 cm gives 5 D, not 0.05 D.
• Using thin lens formulas for thick lenses. The formulas assume the lens thickness is negligible.
• Thinking the angle of deviation of a prism is fixed. It changes with the angle of incidence and has a minimum value.
• Ignoring the surrounding medium. In the lens maker's formula n is the refractive index of the lens relative to the medium, so a glass lens in water has a longer focal length than in air.

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

What is the sign convention used in ray optics?

The textbook uses the Cartesian sign convention. The pole of the mirror or the optical centre of the lens is the origin. Distances measured in the direction of the incident light are positive and those measured against it are negative. Heights above the principal axis are positive and those below are negative. If you apply these rules strictly, the same formula works for every mirror and lens.

How does total internal reflection occur?

Two conditions are needed. Light must travel from a denser medium to a rarer one, and the angle of incidence must be greater than the critical angle. Then no refracted ray exists and all the light is reflected back into the denser medium. Optical fibres use this to carry light signals over long distances with very little loss.

What is the use of the lens maker's formula?

It tells a lens maker what to do to get a required focal length: choose glass of a suitable refractive index and grind its two faces to the right radii of curvature. Spectacle lenses and camera lenses are designed this way.

Why does a prism disperse white light?

The refractive index of glass is different for different wavelengths. It is larger for violet light, which has a shorter wavelength, than for red light. So violet slows down more and bends more than red, and the colours in white light come out of the prism in different directions as a spectrum.

What is the difference between power and magnification?

Power tells you how strongly a lens converges or diverges light and equals 1/f in dioptre. Magnification is the ratio of image height to object height. Power is fixed for a given lens, but magnification changes with where you place the object, so a powerful lens does not always give a large image.

Why is the sky red during sunrise and sunset?

Near the horizon, sunlight travels through a much thicker layer of air. Blue and violet light, which are scattered most, are removed from the direct beam along the way. The red and orange light, which is scattered least, reaches our eyes, so the sun and the sky around it look red.