Ray Optics Online Test 12th Science Questions

Light is mystical. Yet, its behaviour is so fascinating. It is difficult to comprehend light to a single entity. In this unit, we learn it in two different scientific aspects called ray optics and wave optics. Ray optics deals with light that is represented as a ray travelling in straight lines. In wave optics, we study about the phenomenon associated with the propagation of light as a wave.

Light travels in a straight line in a medium. Light may deviate in its path only when it encounters another medium or an obstacle.

A ray of light gives information about only the direction of light. It does not give information about the other characteristics of light like intensity and colour.

The path of the light is called a ray of light and a bundle of such rays is called a beam of light. In this chapter, we can explain the phenomena of reflection, refraction, dispersion and scattering of light, using the ray depiction of light.

The bouncing back of light into the same medium when it encounters a reflecting surface is called reflection of light.

Polished surfaces can reflect light. Mirrors which are silver coated at their back can reflect almost 90% of the light falling on them.

According to law of reflection,
(a) The incident ray, reflected ray and normal to the reflecting surface all are coplanar (ie. lie in the same plane).
(b) The angle of incidence i is equal to the angle of reflection r
i = r

The law of reflection is valid at each point for any reflecting surface whether the surface is plane or curved. The angle between the incident and deviated light ray is called angle of deviation of the light ray.

If the reflecting surface is flat, then incident parallel rays after reflection come out parallel as per the law of reflection. If the reflecting surface is irregular, then the incident parallel rays after reflection come out irregular (not parallel) rays.

The angle between the incident and deviated light ray is called angle of deviation of the light ray. The incident light is AO. The reflected light is OB. The un-deviated light is OC which is the continuation of the incident light. The angle between OB and OC is the angle of deviation d. From the geometry, it is written as, d = 180 – (i+r). As, i = r in reflection, we can write angle of deviation in reflection at plane surface as,
d = 180 – 2i

When a real object is placed at a point O in front of a plane mirror it produces divergent rays in all directions as shown in Figure

After reflection from the plane mirror, they appear to come out from a point I behind the mirror. This image cannot be formed on a screen as the image is behind the mirror. This type of image which cannot be formed on the screen but can only be seen with the eyes is called virtual image

On the other hand, if convergent rays are incident on a plane mirror, the rays after reflection pass through a point I in front of the mirror and form an image as shown in Figure. This image can be formed on a screen as the image is in front of the mirror. This type of image which can be formed on a screen and can also be seen with the eyes is called real image.

It is generally known that a plane mirror can only form a virtual image. But now we have understood that a plane mirror can form a real image when converging rays fall on it.

A spherical surface is a part cut from a hollow sphere. Spherical mirrors are generally constructed from glass. One surface of the glass is silvered. The reflection takes place at the other polished surface.

If the reflection takes place at the convex surface, it is called a convex mirror and if the reflection takes place at the concave surface, it is called a concave mirror.

The radius of the sphere of which the spherical mirror is a part is called the radius of curvature (R) of the mirror. The middle point on the spherical surface of the mirror (or) the geometrical centre of the mirror is called pole (P) of the mirror.

The line joining the pole and the centre of curvature is called the principal axis of the mirror. The light ray travelling along the principal axis towards the mirror after reflection travels back along the same principal axis. It is also called optical axis.

Light rays travelling parallel and close to the principal axis when incident on a spherical mirror, converge at a point for concave mirror or appear to diverge from a point for convex mirror on the principal axis. This point is called the focus or focal point (F) of the mirror.

The distance between the pole and the focus is called the focal length (f) of the mirror. The plane through the focus and perpendicular to the principal axis is called the focal plane of the mirror.

The rays travelling very close to the principal axis and make small angles with it are called paraxial rays. The paraxial rays fall on the mirror very close to the pole of the mirror.

On the other hand, the rays travelling far away from the principal axis and fall on the mirror far away from the pole are called as marginal rays. Both Paraxial rays and marginal rays behave differently (get focused at different points).

PF is focal length f and PC is the radius of curvature R.

A ray parallel to the principal axis after reflection will pass through or appear to pass through the principal focus. A ray passing through or appear to pass through the principal focus, after reflection will travel parallel to the principal axis.

A ray passing through the centre of curvature retraces its path after reflection as it is a case of normal incidence. A ray falling on the pole will get reflected as per law of reflection keeping principal axis as the normal.

While tracing the image, we would normally come across the object distance u, the image distance v, the object height h, the image height (h′), the focal length f and the radius of curvature R.

Cartesian sign convention:
• The Incident light is taken from left to right (i.e. object on the left of mirror).
• All the distances are measured from the pole of the mirror (pole is taken as origin).

Cartesian sign convention:
• The distances measured to the right of pole along the principal axis are taken as positive.
• The distances measured to the left of pole along the principal axis are taken as negative.
• Heights measured in the upward perpendicular direction to the principal axis are taken as positive.
• Heights measured in the downward perpendicular direction to the principal axis, are taken as negative.

The following equation is mirror equation:

The lateral or transverse magnification is defined as the ratio of the height of the image to the height of the object. Height of the object and image are measured perpendicular to the principal axis

Light travels with the highest speed in vacuum. The speed of light in vacuum is denoted as c and its value is, c = 3×108 ms-1. It is a very high value. Several attempts were made by scientists to determine the speed of light. The earliest attempt was made by a French scientist Hippolyte Fizeau (1819– 1896). That paved way for the other scientists too to determine the speed of light.

In Fizeau’s method to determine speed of light, e light from the source S was first allowed to fall on a partially silvered glass plate G kept at an angle of 45o to the incident light from the source.

Fizeau had some difficulty to visually estimate the minimum intensity of the light when blocked by the adjacent tooth, and his value for speed of light was very close to the actual value. Later on, with the same idea of Fizeau and with much sophisticated instruments, the speed of light in air was determined as, v = 2.99792×10⁸ m s^–1.

Different transparent media like glass, water etc. were introduced in the path of light by scientists like Foucault (1819– 1868) and Michelson (1852–1931) to find the speed of light in different media.

Refractive index of a transparent medium is defined as the ratio of speed of light in vacuum (or air) to the speed of light in that medium.

Refractive index does not have unit. The smallest value of refractive index is for vacuum, which is 1. For any other medium refractive index is greater than 1.

Refractive index is also called as optical density of the medium. Higher the refractive index of a medium, greater is its optical density and speed of light through the medium is lesser and vice versa.

Refraction is passing through of light from one optical medium to another optical medium through a boundary. In refraction, the angle of incidence i in one medium and the angle of reflection r in the other medium are measured with respect to the normal drawn to the surface at the point of incidence of light. Law of refraction is called Snell’s law

The ratio of angle of incident i in the first medium to the angle of reflection r in the second medium is equal to the ratio of refractive index of the second medium n₂ to that of the refractive index of the first medium n₁.

We know that the angle between the incident and deviated light is called angle of deviation. When light travels from rarer to denser medium it deviates towards normal as shown in Figure 6.16. The angle of deviation in this case is,

Characteristics of refraction:
• When light passes from rarer medium to denser medium it deviates towards normal in the denser medium.
• When light passes from denser medium to rarer medium it deviates away from normal in the rarer medium.

The phenomenon in which a part of light from a source undergoing reflection and the other part of light from the same source undergoing refraction at the same surface is called simultaneous reflection or simultaneous refraction. Such surfaces are available as partially silvered glasses.\

Production of optical surfaces capable of refracting as well as reflecting is possible by properly coating the surfaces with suitable materials. Thus, a glass can be made partially see through and partially reflecting by varying the amount of coating on its surface.

Partially reflecting mirror is commercially called as two-way mirror, half-silvered or semi-silvered mirror etc.

Partially reflecting mirror is commercially called as two-way mirror, half- silvered or semi-silvered mirror etc. This gives a perception of regular mirror if the other side is made dark. But still hidden cameras can be kept behind such mirrors. We need to be cautious when we stand in front of mirrors kept in unknown places.

We need to be cautious when we stand in front of mirrors kept in unknown places. There is a method to test the two-way mirror. Place the finger nail against the mirror surface. If there is a gap between nail and its image, then it is a regular mirror. If the fingernail directly touches its image, then it is a two-way mirror.

When a ray passes from an optically denser medium to an optically rarer medium, it bends away from normal. Because of this, the angle of refraction r on the rarer medium is greater than the corresponding angle of incidence i in the denser medium. As angle of incidence i is gradually increased, r rapidly increases and at a certain stage it becomes 90° or gracing the boundary.

Due to refraction of light through different layers of atmosphere which vary in refractive index, the path of light deviates continuously when it passes through atmosphere. For example, the Sun is visible a little before the actual sunrise and also until a little after the actual sunset due to refraction of light through the atmosphere. By actual sunrise what we mean is the actual crossing of the sun at the horizon

The apparent shift in the direction of the sun is around half a degree and the corresponding time difference between actual and apparent positions is about 2 minutes. Sun appears flattened (oval shaped) during sun rise and sunset due to the same phenomenon.

If the angle of incidence in the denser medium is increased beyond the critical angle, there is no refraction possible in to the rarer medium. The entire light is reflected back into the denser medium itself. This phenomenon is called total internal reflection.

The two conditions for total internal reflection are,

(a) light must travel from denser to rarer medium,

(b) angle of incidence in the denser medium must be greater than critical angle (i>i_c).

Refractive index of glass is about 1.5. The critical angle for glass-air interface is

The critical angle for water-air interface is,

Diamond appears dazzling because the total internal reflection of light happens inside the diamond. The refractive index of only diamond is about 2.417.

Diamond is much larger than that for ordinary glass which is about only 1.5. The critical angle of diamond is about 24.4°. It is much less than that of glass. A skilled diamond cutter makes use of this larger range of angle of incidence (24.4° to 90° inside the diamond), to ensure that light entering the diamond is total internally reflected from the many cut faces before getting out.

The refractive index of air increases with its density. In hot places, air near the ground is hotter than air at a height. Hot air is less dense.

In the cold places the refractive index increases towards the ground because the temperature of air close to the ground is lesser than the temperature above the surface of earth. Thus, the density and refractive index of air near the ground is greater than at a height.

In the cold regions like glaciers and frozen lakes and seas, the reverse effect of mirage will happen. Hence, an inverted image is formed little above the surface.

When a light source like electric bulb is kept inside a water tank, the light from the source travels in all direction inside the water. The light that is incident on the water surface at an angle less than the critical angle will undergo refraction and emerge out from the water. The light incident at an angle greater than critical angle will undergo total internal reflection.The light falling particularly at critical angle graces the surface.

Transmitting signals through optical fibres is possible due to the phenomenon of total internal reflection. Optical fibres consists of inner part called core and outer part called cladding (or) sleeving

The refractive index of the material of the core must be higher than that of the cladding for total internal reflection to happen. Signal in the form of light is made to incident inside the core-cladding boundary at an angle greater than the critical angle. Hence, it undergoes repeated total internal reflections along the length of the fibre without undergoing any refraction.

To ensure the critical angle incidence in the core-cladding boundary inside the optical fibre, the light should be incident at a certain angle at the end of the optical fiber while entering in to it. This angle is called acceptance angle

An endoscope is an instrument used by doctors which has a bundle of optical fibres that are used to see inside a patient’s body. Endoscopes work on the phenomenon of total internal reflection. The optical fibres are inserted in to the body through mouth, nose or a special hole made in the body. Even operations could be carried out with the endoscope cable which has the necessary instruments attached at their ends.

The refractions also do take place at spherical surface between two transparent media. The laws of refraction hold good at every point on the spherical surface. The normal at the point of incidence is perpendicular to the tangent plane to the spherical surface at that point.

The following assumptions are made while considering refraction at spherical surfaces.
(a) The incident light is assumed to be monochromatic (single colour)
(b) The incident ray of light is very close to the principal axis (paraxial rays).

A lens is formed by a transparent material bounded between two spherical surfaces or one plane and another spherical surface. In a thin lens, the distance between the surfaces is very small. If there are two spherical surfaces, then there will be two centres of curvature C₁ and C₂ and correspondingly two radii of curvature R₁ and R₂.

The primary focus F1 is defined as a point where an object should be placed to give parallel emergent rays to the principal axis. For a convergent lens, such an object is a real object and for a divergent lens, it is a virtual object. The distance PF1 is the primary focal length f1 . The secondary focus F2 is defined as a point where all the parallel rays travelling close to the principal axis converge to form an image on the principal axis. For a convergent lens, such an image is a real image and for a divergent lens, it is a virtual image. The distance PF2 is the secondary focal length f 2.

The sign of focal length is not decided on the direction of measurement of the focal length from the pole of the lens as they have two focal lengths, one to the left and another to the right (primary and secondary focal lengths on either side of the lens). The focal length of the thin lens is taken as positive for a converging lens and negative for a diverging lens.

This equation is known as lens equation which relates the object distance u and image distance v with the focal length f of the lens. This formula holds good for a any type of lens

Power of lens is the measurement of deviating strength of a lens i.e. when a ray is incident on a lens then the degree with which the lens deviates the ray is determined by the power of the lens. Power of the lens is inversely proportional to focal length i.e. greater the power of lens, greater will be the deviation of ray and smaller will be the focal length.

Given, focal length of first lens, f₁ = –70 cm, focal length of second lens, f ₂ = 150 cm.

Given, focal length of first lens, f₁ = –70 cm, focal length of second lens, f ₂ = 150 cm.

System of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments. They produce better magnification as well as sharpness of the images.

A prism is a triangular block of glass or plastic. It is bounded by the three plane faces not parallel to each other. Its one face is grounded which is called base of the prism. The other two faces are polished which are called refracting faces of the prism. The angle between the two refracting faces is called angle of prism (or) refracting angle (or) apex angle of the prism.

The angle of deviation depends on these following factors:
(i) the angle of incidence
(ii) the angle of the prism
(iii) the material of the prism
(iv) the wave length of the light

So far the angle of deviation produced by a prism is discussed for monochromatic light (i.e. light of single colour). When white light enter in to a prism, the effect called dispersion takes place. Dispersion is splitting of white light into its constituent colours. This band of colours of light is called its spectrum.

When a narrow beam of parallel rays of white light is incident on the face of a prism and the refracted beam is received on a white screen, a band of colours is obtained in the order, recollected by the word: VIBGYOR i.e., Violet, Indigo, Blue, Green, Yellow, Orange and Red. Violet is the most deviated and red is the least deviated colour.

The colours obtained in a spectrum depend on the nature of the source of the light used. Each colour of light is associated with a definite wavelength.

Red light is at the longer wavelength end (700 nm) while the violet light is at the shorter wavelength end (400 nm). Therefore the violet ray travels with a smaller velocity in glass prism than red ray.

Sir Isaac Newton has demonstrated through a classic experiment to produce white light when all the colours of VIBGYOR are recombined. He used a prism to produce dispersion and made all the colours to incident on another inverted prism to combine all the colours to get white light.

Dispersion takes place because light of different wave lengths travel with different speeds inside the prism. . In Vacuum, all the colours travel with the same speed. The refractive index of two different glasses for different colours.

In other words, the refractive index of the material of the prism is different for different colours. For violet, the refractive index is high and for red the refractive index is the low.

The speed of light is independent of wavelength in vacuum. Therefore, vacuum is a non-dispersive medium in which all colours travel with the same speed.

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When sunlight enters the atmosphere of the earth, the atmospheric particles present in the atmosphere change the direction of the light. This process is known as scattering of light.

If the scattering of light is by atoms and molecules which have size a very less than that of the wave length λ of light a<< λ, scattering is called Rayleigh’s scattering. The intensity of Rayleigh’s scattering is inversely proportional to fourth power of wavelength.

According to equation, violet colour which has the shortest wavelength gets much scattered during day time. The next scattered colour is blue. As our eyes are more sensitive to blue colour than violet colour the sky appears blue during day time. But, during sunrise and sunset, the light from sun travels a greater distance through the atmosphere. Hence, the blue light which has shorter wavelength is scattered away and the less-scattered red light of longer wavelength manages to reach our eye.

Primary rainbow is formed when light entering the drop undergoes one total internal reflection inside the drop before coming out from the drop as shown in figure. The angle of view for violet to red in primary rainbow is 40^o to 42^o.

A secondary rainbow appears outside of a primary rainbow and develops when light entering a raindrop undergoes two internal reflections. The angle of view for red to violet in a secondary rainbow is, 52^o to 54^o.

Rainbow is an example of dispersion of sunlight through droplets of water during rainy days. Rainbow is observed during a rainfall or after the rainfall or when we look at a water fountain provided the sun is at the back of the observer. When sunlight falls on the water drop suspended in air, it splits (or dispersed) into its constituent seven colours.

If earth has no atmosphere there would not have been any scattering and the sky would appear dark. That is why sky appears dark for the astronauts who could see the sky from above the atmosphere.

In clouds all the colours get equally scattered irrespective of wavelength. This is the reason for the whitish appearance of cloud as shown. But, the rain clouds appear dark because of the condensation of water droplets on dust particles that makes the cloud become opaque.

Light is a form of energy that is transferred from one place to another. A glance at the evolution of various theories of light put forward by scientists will give not only an over view of the nature of light but also its propagation and some phenomenon demonstrated by it.

Sir Isaac Newton (1672) gave the corpuscular theory of light which was also suggested earlier by Descartes (1637) to explain the laws of reflection and refraction.

According this theory, light is emitted as tiny, massless (negligibly small mass) and perfectly elastic particles called corpuscles. As the corpuscles are very small, the source of light does not suffer appreciable loss of mass even if it emits light for a long time. On account of high speed, they are unaffected by the force of gravity and their path is a straight line in a medium of uniform refractive index.

On account of high speed, they are unaffected by the force of gravity and their path is a straight line in a medium of uniform refractive index. The energy of light is the kinetic energy of these corpuscles. When these corpuscles impinge on the retina of the eye, the vision is produced.

Corpuscular theory could not explain the reason why the speed of light is lesser in denser medium than in rarer medium and also the phenomena like interference, diffraction and polarisation.