1. Optics: The study of nature and propagation of light is called optics. Ray optics deals with particle nature of light whereas wave optics considers light as a wave.
2. (a) Reflection:
When a light ray incident on a smooth surface bounces back to the same medium, it is called reflection of light.
(b) Laws of regular Reflection:
(i) Angle of incidence is equal to the angle of reflection.
i.e., i = r
(ii) The incident ray, the reflected ray and the normal at the point of incidence, all lie in the same plane.
These laws hold for any reflecting surface whether plane or curved.
There is no change in wavelength and frequency during reflection.
(c) Spherical Mirror: A spherical mirror is simply a part cut off from the surface of a hollow sphere which has been made smooth and silver polished on one side.
Spherical mirrors are of two types:
(i) Concave mirror: If outer side or bulging side of the spherical surface is silver polished, it is called a concave mirror.
(ii) Convex mirror: If inner side of a spherical surface is silver polished, it is called a convex mirror.
(d) Relation between focal length and radius of curvature: The distance between centre (C) of spherical surface and its pole (P) is called the radius of curvature. It is denoted by R.
The rays parallel to the principal axis (CP) after striking the mirror meet at a point (F) (in concave mirror) or appear to be meeting at a point F (in convex mirror). This point is called the principal focus (F) of mirror. The distance of focus (F) from pole (P) of a mirror is called the focal length of the mirror. It is denoted by f. The focal length f is half of the radius of curvature.
i.e.,
(e) Mirror formula: The mirror formula is
where u = distance of object from mirror;
v= distance of image from mirror;
and f = focal length of mirror.
(f) Magnification produced by mirror: The ratio of the size of image to the size of object is called linear magnification produced by the mirror.
Magnification
Where I is the height of image and O is the height of object.
3. Refraction of Light
When a ray of light enters from one transparent medium into another, there is a change in speed and direction of the ray in the second medium. This phenomenon is called refraction of light.
Laws of refraction:
(i) The incident ray, the refracted ray and the normal to the surface separating the two media, all lie in the same plane.
(ii) Snell’s Law: For two media, the ratio of sine of angle of incidence to the sine of the angle of refraction is constant for a beam of particular wavelength, i.e.,
where n1 and n2 are absolute refractive indices of I and II media respectively and 1n2 is a refractive index of second (II) medium with respect to first (I) medium.
Due to principle of reversibility of light,
Multiplying (i) by (ii), we get
The frequency of light remains unchanged while passing from one medium to the other.
Refractive Index
The refractive index of a medium is defined as the ratio of speed of light in vacuum to the speed of light in a medium.
i.e.,
λair and λmedium being wavelengths of light in air and medium respectively.
∴
Formation of image due to refraction: According to Snell’s law, if n2 > n1, i > r. That is, if a ray of light enters from rarer medium to a denser medium, it is deviated towards the normal and if n2 < n1, i < r that is, if the ray of light enters from denser to a rarer medium it is deviated away from the normal.
Accordingly, if the ray of light starting from object O, in the given diagram in a denser medium travels along OP, it is deviated away from the normal along PQ. The ray PQ appears to come from I. Thus I is the virtual image of O. It can be shown that
i.e.,
where x is the apparent shift.
∴ The apparent shift,
Refraction through a number of media: Let us consider the refraction of light ray through a series of media as shown in fig. The ray AB is incident on air-water interface at an angle i. The ray is deviated in water along BC towards the normal. Then it falls on water-glass interface and is again deviated towards normal along CD. If the last medium is again air, the ray emerges parallel to the incident ray. Let r1 and r2 be angles of refraction in water and glass respectively, then from Snell’s law,
Multiplying (i), (ii) and (iii), we get anw × wng × gna=1
4. Critical Angle
When a ray of light is incident on the interface from denser medium to rarer medium, it is deviated away from the normal. When angle of incidence is increased, angle of refraction also increases and at a stage it becomes 90°.
The angle of incidence in denser medium for which the angle of refraction in rarer medium is 90° is called the critical angle (C) for the pair of media.
If nr and nd are refractive indices for rarer and denser media, then
∴
sin
where rnd = n and n is the refractive index of a denser medium with respect to a rarer medium.
5. Total Internal Reflection
When angle of incidence in the denser medium is greater than the critical angle, the incident ray does not refract into a rarer medium but is reflected back into the denser medium. This phenomenon is called total internal reflection. The conditions for total internal reflection are
(i) The ray must travel from a denser into a rarer medium.
(ii) The angle of incidence i> critical angle C.
The critical angle for water-air, glass-air and diamond-air interfaces are 49°, 42° and 24° respectively.
6. Spherical Lenses
There are two types of spherical lenses.
(i) Convex lens (Converging lens)
(ii) Concave lens (Diverging lens)
Rules of Image Formation in Lenses
(i) The ray incident on lens parallel to the principal axis, after refraction through the lens, passes through the second focus (in convex lens) or appear to come from second focus in concave lens.
(ii) The ray incident on lens through optical centre C, after refraction, pass straight without any deviation.
(iii) A ray directed towards the first focus incident on the lens, after refraction becomes parallel to the principal axis.
7. Thin Lens Formula
If u and v are object and image distances from a lens of focal length f, then thin lens formula is
This equation holds for convex and concave lenses both, but proper signs of u, v and f are to be used according to sign convention of coordinate geometry. Focal length of a convex lens is taken as positive and of a concave lens is taken as negative.
Magnification produced by a lens
where I is the size of image and O is the size of object.
8. Lens Maker’s Formula
If R1 and R2 are the radii of curvature of first and second refracting surfaces of a thin lens of focal length f, then lens makers formula is
where 1n2=n is refractive index of material of lens with respect to surrounding medium.
9. Power of a Lens
The power of a lens is its ability to deviate the rays towards its principal axis. It is defined as the reciprocal of focal length in metres.
Power of a lens,
Its unit is diopter and is represented as ‘D’.
10. Lens Immersed in a Liquid
If a lens of refractive index ng is immersed in a liquid of refractive index nl then its focal length (fl) in liquid, is given by
where
If fa is the focal length of lens in air, then
Three cases arise:
(i) If ng > nl , then fl and fa are of same sign but fl > fa.
That is, the nature of lens remains unchanged, but its focal length increases and hence the power of lens decreases. In other words the convergent lens becomes less convergent and divergent lens becomes less divergent.
(ii) If ng = nl, then f1 = ∞. That is, the lens behaves as a glass plate.
(iii) If ng < nl, then fl and fa have opposite signs.
That is, the nature of lens changes. A convergent lens becomes divergent and vice versa.
11. Thin Lenses in Contact
If two or more lenses of focal lengths f1, f2 are placed in contact, then their equivalent focal length F is given by
The power of combination
P = P1 + P2 + ... = ∑P.
12. Combination of a Lens and a Mirror
Consider a coaxial arrangement of a lens and a mirror. Let an object be placed in front of the lens. The incident rays, from the object, first undergo refraction at lens and are then incident on the mirror. To obtain the position of the image due to the combination, we can proceed as follows:
(i) Using refraction formula, we can calculate where the image would have been formed, had there been only the lens. We then consider this image as an object for the mirror.
(ii) Using the mirror formula, we can then locate the position of its final image formed by the mirror. This final position, would be the position of the image due to the combined effect of refraction at the lens and reflection at the mirror.
13. Refraction Through a Prism
A prism is a transparent medium enclosed by two plane refracting surfaces. Let EF be the monochromatic ray incident on the face PQ of prism PQR of refracting angle A at angle of incidence i1. This ray is refracted along FG, r1 being angle of refraction. The ray QG is incident on the face PR at angle of incidence r2 and is refracted in air along GH. Thus GH is the emergent ray and i2 is the angle of emergence. The angle between incident ray EF and emergent ray GH is called angle of deviation δ.
For a prism if A is the refracting angle of prism, then
r1 + r2 = A …(i)
and i1 + i2 = A + δ …(ii)
Clearly, deviation δ = i1+ i2 – A, i1 and i2 may be inter-changed, therefore, there are two values of angles of incidence for same deviation δ.
If n is the refractive index of material of prism, then from Snell’s law
If angle of incidence is changed, the angle of deviation δ changes as shown in fig. For a particular angle of incidence the deviation is minimum. This is called angle of minimum deviation δm.
Minimum deviation: At minimum deviation the refracted ray within a prism is parallel to the base. Therefore,
i1 = i2 = i (say)
r1 = r2 = r (say)
Then from equations (i) and (ii),
r + r = A or r = A/2 …[iv (a)]
∴ The refractive index of material of prism
For a thin prism, viz. A ≤ 10°.
δm= (n – 1) A.
14. Scattering of Light
The light is scattered by air molecules. According to Lord Rayleigh the intensity of scattered light
As λblue < λred accordingly blue colour is scattered the most and red the least, so sky appears blue.
At the time of sunrise and sunset, blue colour is scattered the most and red colour enters our eyes, so sunrise and sunset appear red.
15. Optical Instruments (Microscopes and Telescopes)
A microscope is an optical instrument to see very small objects.
(i) Simple Microscope: It consists of a convex lens of small focal length f.
If β = angle subtended by an image on eye
a = angle subtended by an object on eye, when object is at a distance of distinct vision (D)
Magnifying power,
If the final image is at ∞, v = ∞ then
If the final image is at a distance of distinct vision,
(ii) Compound Microscope: A compound microscope essentially consists of two co-axial convex lenses of small focal lengths. The lens facing the object is called an objective lens while that towards eye is called the eye lens. (eyepiece).
∴ Magnifying power of microscope,
Separation between lenses, L = v0 + ue
Special cases:
(a) When final image is formed at a distance of distinct vision, ve = D
The distance between second focal point of objective and first focal point of eye lens is called the tube length denoted by L,then
So,
(b) When final image is formed at infinity, ve= ∞, then
Telescope: It is an optical instrument to see distant objects.
(iii) Astronomical Telescope (Refracting Telescope): It is used to see magnified images of distant objects. An astronomical telescope essentially consists of two co-axial convex lenses. The lens facing the object has a large focal length and a large aperture and is called objective, while the lens towards eye has a small focal length and small aperture and is called eye lens.
The magnifying power of telescope is
and Length of telescope L=f0+ue
where ue = distance of real image from eye lens
ve = distance of final image A′ B′ from eye lens
f0 = focal length of objective, fe= focal length of eye lens
α = angle subtended by an object at eye =
β = angle subtended by an image at eye =
Special cases:
(a) When final image is formed at a distance of distinct vision, then ve=D
(b) When final image is formed at infinity, then ve= ∞
Reflecting Telescope: In this telescope, a concave mirror is used as an objective in place of a convex lens. It is free from chromatic aberration and it has larger resolving power than refracting telescope.
16. Magnifying Power of Optical Instruments
The size of an object depends on the angle subtended by the object on eye. This angle is called visual angle. Greater the visual angle, greater the size of object. Stars are bigger than sun; but appear smaller because stars are much farther away than sun and they subtend smaller angles on eye.
The angle subtended on eye may be increased by using telescopes and microscopes. The telescopes and microscopes form the image of an object. The image subtends larger angle on eye; hence the object appears big. The magnification produced by optical instrument (telescope/microscope) is defined as the ratio of angle (β) subtended by image on eye and the angle (a) subtended by object on eye.
i.e., Angular magnification
Comments
Post a Comment